LMFDB - Space of modular forms of level 5929, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 60 $
Sturm bound:			$1232$
Trace bound:			$18$
Distinguishing $T_p$:			$2$, $3$, $5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5929))$.

	Total	New	Old
Modular forms	664	395	269
Cusp forms	569	350	219
Eisenstein series	95	45	50

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

$7$	$11$	Fricke	Dim
$+$	$+$	$+$	$80$
$+$	$-$	$-$	$92$
$-$	$+$	$-$	$93$
$-$	$-$	$+$	$85$
Plus space		$+$	$165$
Minus space		$-$	$185$

Trace form

$ 350 q - 2 q^{2} + 2 q^{3} + 324 q^{4} - 2 q^{5} - 6 q^{6} + 308 q^{9} + O(q^{10}) $

$ 350 q - 2 q^{2} + 2 q^{3} + 324 q^{4} - 2 q^{5} - 6 q^{6} + 308 q^{9} - 4 q^{10} + 20 q^{12} + 2 q^{13} + 10 q^{15} + 268 q^{16} - 4 q^{17} - 4 q^{18} - 12 q^{20} + 6 q^{23} - 16 q^{24} + 250 q^{25} + 24 q^{26} + 14 q^{27} + 8 q^{29} + 46 q^{30} + 18 q^{31} + 28 q^{32} + 236 q^{36} - 28 q^{37} + 12 q^{38} - 16 q^{39} + 6 q^{40} - 18 q^{41} + 18 q^{43} - 4 q^{45} + 18 q^{46} + 20 q^{47} + 12 q^{48} + 22 q^{51} + 26 q^{52} - 26 q^{53} - 34 q^{54} + 8 q^{57} - 22 q^{58} - 6 q^{59} + 76 q^{60} - 10 q^{61} + 6 q^{62} + 112 q^{64} - 28 q^{65} + 2 q^{67} - 6 q^{68} - 2 q^{69} - 18 q^{71} + 40 q^{72} + 2 q^{73} - 30 q^{74} + 48 q^{75} + 20 q^{76} - 30 q^{79} + 72 q^{80} + 198 q^{81} + 8 q^{82} + 22 q^{83} - 66 q^{85} + 72 q^{86} - 60 q^{87} + 14 q^{89} + 42 q^{90} + 100 q^{92} + 22 q^{93} - 36 q^{94} + 40 q^{95} + 32 q^{96} + 26 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5929))$ 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5929.2.a.a	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}+3q^{8}+\cdots$
5929.2.a.b	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}+2q^{5}+2q^{6}+3q^{8}+\cdots$
5929.2.a.c	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$-1$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{16}+3q^{18}+\cdots$
5929.2.a.d	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots$
5929.2.a.e	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$1$	$3$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+q^{3}-2q^{4}+3q^{5}-2q^{9}-2q^{12}+\cdots$
5929.2.a.f	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{4}+q^{5}+6q^{9}-6q^{12}+\cdots$
5929.2.a.g	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-3q^{8}+\cdots$
5929.2.a.h	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{9}+\cdots$
5929.2.a.i	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$1$	$-2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1-\beta )q^{3}+3\beta q^{4}+\cdots$
5929.2.a.j	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
5929.2.a.k	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-1$	$1$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+\beta q^{3}+(1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
5929.2.a.l	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
5929.2.a.m	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$4$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{3}+3q^{4}+2q^{5}+\cdots$
5929.2.a.n	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{11}) $	$\Q(\sqrt{-11}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{3}-2q^{4}+\beta q^{5}+8q^{9}-2\beta q^{12}+\cdots$
5929.2.a.o	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
5929.2.a.p	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+(1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
5929.2.a.q	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$2$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
5929.2.a.r	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-\beta q^{6}-3q^{8}+\cdots$
5929.2.a.s	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$1$	$-2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots$
5929.2.a.t	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.568.1	None	✓	$1$	$0$	$-2$	$1$	$-1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots$
5929.2.a.u	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$-6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
5929.2.a.v	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.257.1	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
5929.2.a.w	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.257.1	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
5929.2.a.x	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$3$	$6$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
5929.2.a.y	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.568.1	None	✓	$1$	$0$	$2$	$1$	$-1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots$
5929.2.a.z	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.4400.1	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
5929.2.a.ba	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.9248.1	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
5929.2.a.bb	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.2525.1	None	✓	$1$	$1$	$-2$	$2$	$6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bc	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.6125.1	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(\beta _{2}+\beta _{3})q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{8}+\cdots$
5929.2.a.bd	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	$\Q(\sqrt{2}, \sqrt{11})$	$\Q(\sqrt{-11}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-\beta _{1}q^{3}-2q^{4}+(\beta _{1}+\beta _{2})q^{5}+(3+\beta _{3})q^{9}+\cdots$
5929.2.a.be	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	$\Q(\zeta_{24})^+$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}-2\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots$
5929.2.a.bf	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+3q^{4}+\beta _{1}q^{5}-\beta _{3}q^{8}-3q^{9}+\cdots$
5929.2.a.bg	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.6125.1	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{2}+(2-\beta _{2}+\beta _{3})q^{4}+(2\beta _{1}+2\beta _{2}+\cdots)q^{8}+\cdots$
5929.2.a.bh	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.4400.1	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
5929.2.a.bi	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	4.4.2525.1	None	✓	$1$	$0$	$2$	$2$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bj	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.7674048.1	None	✓	$1$	$0$	$-4$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bk	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.58383808.1	None	✓	$2$	$1$	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bl	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.58383808.1	None	✓	$2$	$0$	$0$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bm	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.7674048.1	None	✓	$1$	$0$	$4$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
5929.2.a.bn	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
5929.2.a.bo	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
5929.2.a.bp	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
5929.2.a.bq	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
5929.2.a.br	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	8.8.$\cdots$.1	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
5929.2.a.bs	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-1$	$-4$	$-10$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
5929.2.a.bt	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$1$	$-4$	$-10$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
5929.2.a.bu	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	8.8.$\cdots$.1	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
5929.2.a.bv	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}-\beta _{1}q^{3}+(2+\beta _{9})q^{4}-\beta _{7}q^{5}+\cdots$
5929.2.a.bw	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-1$	$-3$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
5929.2.a.bx	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-1$	$3$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
5929.2.a.by	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$1$	$-3$	$-2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
5929.2.a.bz	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$1$	$3$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
5929.2.a.ca	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
5929.2.a.cb	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+\beta _{1}q^{3}+(1+\beta _{9})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
5929.2.a.cc	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-\beta _{8}q^{3}+(2-\beta _{10})q^{4}+(\beta _{7}+\cdots)q^{5}+\cdots$
5929.2.a.cd	$5929$	$2$	5929.a	1.a	$1$	$14$	$14$	$47.343$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$2$	$1$	$0$	$-6$	$-8$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
5929.2.a.ce	$5929$	$2$	5929.a	1.a	$1$	$14$	$14$	$47.343$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$2$	$0$	$0$	$6$	$8$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
5929.2.a.cf	$5929$	$2$	5929.a	1.a	$1$	$16$	$16$	$47.343$	16.16.$\cdots$.1	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{12}q^{2}-\beta _{5}q^{3}+(1+\beta _{13})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
5929.2.a.cg	$5929$	$2$	5929.a	1.a	$1$	$24$	$24$	$47.343$		None	✓	$2$	$1$	$-10$	$0$	$0$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
5929.2.a.ch	$5929$	$2$	5929.a	1.a	$1$	$24$	$24$	$47.343$		None	✓	$2$	$0$	$10$	$0$	$0$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5929))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(5929)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(49))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(77))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(121))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(539))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(847))$$^{\oplus 2}$

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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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 60 \)
Sturm bound:			\(1232\)
Trace bound:			\(18\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(80\)
\(+\)	\(-\)	$-$	\(92\)
\(-\)	\(+\)	$-$	\(93\)
\(-\)	\(-\)	$+$	\(85\)
Plus space		\(+\)	\(165\)
Minus space		\(-\)	\(185\)

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Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5929))\) 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	5929.2.a

Level	$5929$
Weight	$2$
Character orbit	5929.a
Rep. character	$\chi_{5929}(1,\cdot)$
Character field	$\Q$
Dimension	$350$
Newform subspaces	$60$
Sturm bound	$1232$
Trace bound	$18$