LMFDB - Space of modular forms of level 9438, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9438 = 2 \cdot 3 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9438.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 88 $
Sturm bound:			$3696$
Trace bound:			$7$
Distinguishing $T_p$:			$5$, $7$, $17$, $19$, $29$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9438))$.

	Total	New	Old
Modular forms	1896	218	1678
Cusp forms	1801	218	1583
Eisenstein series	95	0	95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$11$	$13$	Fricke	Dim
$+$	$+$	$+$	$+$	$+$	$12$
$+$	$+$	$+$	$-$	$-$	$17$
$+$	$+$	$-$	$+$	$-$	$15$
$+$	$+$	$-$	$-$	$+$	$10$
$+$	$-$	$+$	$+$	$-$	$13$
$+$	$-$	$+$	$-$	$+$	$12$
$+$	$-$	$-$	$+$	$+$	$15$
$+$	$-$	$-$	$-$	$-$	$15$
$-$	$+$	$+$	$+$	$-$	$13$
$-$	$+$	$+$	$-$	$+$	$12$
$-$	$+$	$-$	$+$	$+$	$15$
$-$	$+$	$-$	$-$	$-$	$15$
$-$	$-$	$+$	$+$	$+$	$12$
$-$	$-$	$+$	$-$	$-$	$17$
$-$	$-$	$-$	$+$	$-$	$15$
$-$	$-$	$-$	$-$	$+$	$10$
Plus space				$+$	$98$
Minus space				$-$	$120$

Trace form

$ 218 q + 218 q^{4} - 8 q^{5} - 2 q^{6} - 12 q^{7} + 218 q^{9} + O(q^{10}) $

$ 218 q + 218 q^{4} - 8 q^{5} - 2 q^{6} - 12 q^{7} + 218 q^{9} - 4 q^{10} - 2 q^{13} - 4 q^{14} - 4 q^{15} + 218 q^{16} - 4 q^{17} + 4 q^{19} - 8 q^{20} - 4 q^{21} + 8 q^{23} - 2 q^{24} + 206 q^{25} - 12 q^{28} + 28 q^{29} - 8 q^{30} + 4 q^{31} + 24 q^{35} + 218 q^{36} - 12 q^{37} + 20 q^{38} - 4 q^{40} + 32 q^{41} - 12 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 24 q^{47} + 186 q^{49} - 16 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} - 4 q^{56} - 28 q^{57} - 16 q^{58} + 32 q^{59} - 4 q^{60} - 44 q^{61} - 4 q^{62} - 12 q^{63} + 218 q^{64} + 8 q^{65} - 12 q^{67} - 4 q^{68} - 8 q^{69} + 8 q^{70} + 32 q^{71} + 4 q^{73} + 8 q^{74} + 4 q^{76} + 2 q^{78} + 16 q^{79} - 8 q^{80} + 218 q^{81} - 44 q^{82} + 32 q^{83} - 4 q^{84} + 8 q^{86} - 40 q^{89} - 4 q^{90} - 4 q^{91} + 8 q^{92} + 4 q^{93} + 56 q^{95} - 2 q^{96} + 4 q^{97} + 16 q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9438))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9438.2.a.a	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-3$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
9438.2.a.b	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-3$	$3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+3q^{7}+\cdots$
9438.2.a.c	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
9438.2.a.d	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$
9438.2.a.e	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
9438.2.a.f	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$2$	$-4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-4q^{7}+\cdots$
9438.2.a.g	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
9438.2.a.h	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$4$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-4q^{7}+\cdots$
9438.2.a.i	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$4$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-q^{8}+\cdots$
9438.2.a.j	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-5$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-5q^{7}+\cdots$
9438.2.a.k	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+3q^{7}+\cdots$
9438.2.a.l	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-2$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
9438.2.a.m	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
9438.2.a.n	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
9438.2.a.o	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots$
9438.2.a.p	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+2q^{7}+\cdots$
9438.2.a.q	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$4$	$4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots$
9438.2.a.r	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-3$	$-3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
9438.2.a.s	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
9438.2.a.t	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$2$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots$
9438.2.a.u	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
9438.2.a.v	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+2q^{7}+\cdots$
9438.2.a.w	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$4$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots$
9438.2.a.x	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots$
9438.2.a.y	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-2$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
9438.2.a.z	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-2$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots$
9438.2.a.ba	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
9438.2.a.bb	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
9438.2.a.bc	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
9438.2.a.bd	$9438$	$2$	9438.a	1.a	$1$	$1$	$1$	$75.363$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
9438.2.a.be	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-4$	$10$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-2\beta )q^{5}+q^{6}+\cdots$
9438.2.a.bf	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$-2$	$-2$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
9438.2.a.bg	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(1-2\beta )q^{7}+\cdots$
9438.2.a.bh	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{37}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots$
9438.2.a.bi	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$-2$	$-2$	$-1$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-\beta q^{7}+\cdots$
9438.2.a.bj	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots$
9438.2.a.bk	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$4$	$3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+(2-\beta )q^{7}+\cdots$
9438.2.a.bl	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$2$	$-4$	$3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-2\beta )q^{5}-q^{6}+\cdots$
9438.2.a.bm	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$-2$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
9438.2.a.bn	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$2$	$-2$	$3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3\beta q^{7}+\cdots$
9438.2.a.bo	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$-1$	$7$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+(3+\beta )q^{7}+\cdots$
9438.2.a.bp	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$-3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots$
9438.2.a.bq	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots$
9438.2.a.br	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$2$	$4$	$-5$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots$
9438.2.a.bs	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$-2$	$2$	$4$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
9438.2.a.bt	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$6$	$1$	$+$	$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
9438.2.a.bu	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-4$	$-10$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-2\beta )q^{5}-q^{6}+\cdots$
9438.2.a.bv	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
9438.2.a.bw	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{37}) $	None	✓	$1$	$0$	$2$	$-2$	$-2$	$-1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-\beta q^{7}+\cdots$
9438.2.a.bx	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
9438.2.a.by	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots$
9438.2.a.bz	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$2$	$-2$	$-1$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+\beta q^{7}+\cdots$
9438.2.a.ca	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots$
9438.2.a.cb	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$-2$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots$
9438.2.a.cc	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$4$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
9438.2.a.cd	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-4$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-2\beta )q^{5}+q^{6}+\cdots$
9438.2.a.ce	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-2$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3\beta q^{7}+\cdots$
9438.2.a.cf	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-2$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
9438.2.a.cg	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-1$	$-7$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+(-3+\cdots)q^{7}+\cdots$
9438.2.a.ch	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$2$	$2$	$-1$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
9438.2.a.ci	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$0$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots$
9438.2.a.cj	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots$
9438.2.a.ck	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$4$	$5$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+(3-\beta )q^{7}+\cdots$
9438.2.a.cl	$9438$	$2$	9438.a	1.a	$1$	$2$	$2$	$75.363$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$6$	$-1$	$-$	$-$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
9438.2.a.cm	$9438$	$2$	9438.a	1.a	$1$	$3$	$3$	$75.363$	3.3.3957.1	None	✓	$1$	$0$	$-3$	$-3$	$2$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots$
9438.2.a.cn	$9438$	$2$	9438.a	1.a	$1$	$3$	$3$	$75.363$	3.3.316.1	None	✓	$1$	$0$	$-3$	$3$	$3$	$-1$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
9438.2.a.co	$9438$	$2$	9438.a	1.a	$1$	$3$	$3$	$75.363$	3.3.3957.1	None	✓	$1$	$0$	$3$	$-3$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
9438.2.a.cp	$9438$	$2$	9438.a	1.a	$1$	$3$	$3$	$75.363$	3.3.316.1	None	✓	$1$	$0$	$3$	$3$	$3$	$1$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
9438.2.a.cq	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4752.1	None	✓	$1$	$1$	$-4$	$-4$	$-2$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
9438.2.a.cr	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4400.1	None	✓	$1$	$1$	$-4$	$-4$	$2$	$-2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots$
9438.2.a.cs	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4752.1	None	✓	$1$	$1$	$-4$	$4$	$-6$	$6$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots$
9438.2.a.ct	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.8000.1	None	✓	$1$	$0$	$-4$	$4$	$-4$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots$
9438.2.a.cu	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4752.1	None	✓	$1$	$1$	$4$	$-4$	$-2$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{3}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
9438.2.a.cv	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4400.1	None	✓	$1$	$0$	$4$	$-4$	$2$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots$
9438.2.a.cw	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.4752.1	None	✓	$1$	$1$	$4$	$4$	$-6$	$-6$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots$
9438.2.a.cx	$9438$	$2$	9438.a	1.a	$1$	$4$	$4$	$75.363$	4.4.8000.1	None	✓	$1$	$1$	$4$	$4$	$-4$	$4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
9438.2.a.cy	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.76918000.1	None	✓	$1$	$1$	$-6$	$-6$	$1$	$-7$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
9438.2.a.cz	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.128454336.1	None	✓	$1$	$0$	$-6$	$-6$	$2$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{5}q^{7}+\cdots$
9438.2.a.da	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.103160000.1	None	✓	$1$	$1$	$-6$	$6$	$-5$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{5})q^{5}-q^{6}+\cdots$
9438.2.a.db	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.66590000.1	None	✓	$1$	$1$	$-6$	$6$	$2$	$-7$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{4}-\beta _{5})q^{5}+\cdots$
9438.2.a.dc	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.866559168.1	None	✓	$1$	$0$	$-6$	$6$	$6$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
9438.2.a.dd	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.76918000.1	None	✓	$1$	$0$	$6$	$-6$	$1$	$7$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
9438.2.a.de	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.128454336.1	None	✓	$1$	$0$	$6$	$-6$	$2$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+\beta _{5}q^{7}+\cdots$
9438.2.a.df	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.103160000.1	None	✓	$1$	$0$	$6$	$6$	$-5$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{5})q^{5}+q^{6}+\cdots$
9438.2.a.dg	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.66590000.1	None	✓	$1$	$0$	$6$	$6$	$2$	$7$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{4}-\beta _{5})q^{5}+\cdots$
9438.2.a.dh	$9438$	$2$	9438.a	1.a	$1$	$6$	$6$	$75.363$	6.6.866559168.1	None	✓	$1$	$0$	$6$	$6$	$6$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
9438.2.a.di	$9438$	$2$	9438.a	1.a	$1$	$8$	$8$	$75.363$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$-8$	$-3$	$4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
9438.2.a.dj	$9438$	$2$	9438.a	1.a	$1$	$8$	$8$	$75.363$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$-8$	$-3$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9438))$ into lower level spaces

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9438 = 2 \cdot 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9438.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 88 \)
Sturm bound:			\(3696\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(19\), \(29\)

\(2\)	\(3\)	\(11\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(17\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(15\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(10\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(15\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(15\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(13\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(15\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(15\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(12\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(17\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(15\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(10\)
Plus space				\(+\)	\(98\)
Minus space				\(-\)	\(120\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9438))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9438))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	9438.2.a

Level	$9438$
Weight	$2$
Character orbit	9438.a
Rep. character	$\chi_{9438}(1,\cdot)$
Character field	$\Q$
Dimension	$218$
Newform subspaces	$88$
Sturm bound	$3696$
Trace bound	$7$