LMFDB - Space of modular forms of level 8379, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8379 = 3^{2} \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8379.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 76 $
Sturm bound:			$2240$
Trace bound:			$17$
Distinguishing $T_p$:			$2$, $5$, $11$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8379))$.

	Total	New	Old
Modular forms	1152	308	844
Cusp forms	1089	308	781
Eisenstein series	63	0	63

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

$3$	$7$	$19$	Fricke	Dim
$+$	$+$	$+$	$+$	$28$
$+$	$+$	$-$	$-$	$36$
$+$	$-$	$+$	$-$	$36$
$+$	$-$	$-$	$+$	$24$
$-$	$+$	$+$	$-$	$46$
$-$	$+$	$-$	$+$	$42$
$-$	$-$	$+$	$+$	$45$
$-$	$-$	$-$	$-$	$51$
Plus space			$+$	$139$
Minus space			$-$	$169$

Trace form

$ 308 q - q^{2} + 307 q^{4} + 3 q^{5} - 9 q^{8} + O(q^{10}) $

$ 308 q - q^{2} + 307 q^{4} + 3 q^{5} - 9 q^{8} - 2 q^{10} - 3 q^{11} + 6 q^{13} + 289 q^{16} + 13 q^{17} - 2 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 335 q^{25} - 2 q^{26} + 12 q^{29} - 4 q^{31} + 11 q^{32} + 18 q^{34} - 8 q^{37} + 3 q^{38} + 30 q^{40} + 16 q^{41} - 11 q^{43} - 30 q^{44} - 8 q^{46} + 7 q^{47} + q^{50} + 42 q^{52} + 26 q^{53} - 33 q^{55} + 62 q^{58} - 22 q^{59} - 5 q^{61} - 36 q^{62} + 293 q^{64} + 60 q^{65} + 24 q^{67} - 24 q^{68} - 2 q^{71} - 3 q^{73} + 26 q^{74} - 5 q^{76} - 24 q^{79} - 50 q^{80} + 74 q^{82} + 12 q^{83} + 33 q^{85} + 48 q^{86} + 96 q^{88} + 38 q^{89} - 8 q^{92} + 36 q^{94} - 9 q^{95} + 46 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8379))$ 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8379.2.a.a	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$-3$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-4q^{11}+\cdots$
8379.2.a.b	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+2q^{10}-4q^{11}+\cdots$
8379.2.a.c	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots$
8379.2.a.d	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-4q^{11}+\cdots$
8379.2.a.e	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots$
8379.2.a.f	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-2q^{11}+6q^{13}+\cdots$
8379.2.a.g	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+2q^{11}+4q^{13}+\cdots$
8379.2.a.h	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{5}+3q^{11}+2q^{13}+4q^{16}+\cdots$
8379.2.a.i	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{5}+3q^{11}-2q^{13}+4q^{16}+\cdots$
8379.2.a.j	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}-3q^{11}+4q^{13}+4q^{16}+\cdots$
8379.2.a.k	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots$
8379.2.a.l	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}+2q^{11}-q^{16}+\cdots$
8379.2.a.m	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}+2q^{11}+6q^{13}+\cdots$
8379.2.a.n	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots$
8379.2.a.o	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots$
8379.2.a.p	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{5}-6q^{10}-q^{11}+\cdots$
8379.2.a.q	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}+3q^{11}+\cdots$
8379.2.a.r	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots$
8379.2.a.s	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots$
8379.2.a.t	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots$
8379.2.a.u	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots$
8379.2.a.v	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{5}+\cdots$
8379.2.a.w	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots$
8379.2.a.x	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q-2q^{4}+\beta q^{11}-2q^{13}+4q^{16}+\beta q^{17}+\cdots$
8379.2.a.y	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q-2q^{4}-\beta q^{11}+2q^{13}+4q^{16}+\beta q^{17}+\cdots$
8379.2.a.z	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2\beta q^{5}-2\beta q^{8}-4q^{10}+(3+\cdots)q^{11}+\cdots$
8379.2.a.ba	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2\beta q^{5}-2\beta q^{8}+4q^{10}+(3+\cdots)q^{11}+\cdots$
8379.2.a.bb	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots$
8379.2.a.bc	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-2\beta q^{13}+\cdots$
8379.2.a.bd	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}+2\beta q^{13}+\cdots$
8379.2.a.be	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots$
8379.2.a.bf	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$1$	$0$	$-6$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-3q^{5}+3q^{8}-3\beta q^{10}+\cdots$
8379.2.a.bg	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots$
8379.2.a.bh	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
8379.2.a.bi	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots$
8379.2.a.bj	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots$
8379.2.a.bk	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots$
8379.2.a.bl	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(3+\beta )q^{8}+\cdots$
8379.2.a.bm	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1+2\beta )q^{5}+\cdots$
8379.2.a.bn	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots$
8379.2.a.bo	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.229.1	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
8379.2.a.bp	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.148.1	None	✓	$1$	$1$	$-1$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$
8379.2.a.bq	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.404.1	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.br	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.1957.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
8379.2.a.bs	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	$\Q(\zeta_{24})^+$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots$
8379.2.a.bt	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.1957.1	None	✓	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.bu	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.5744.1	None	✓	$1$	$1$	$0$	$0$	$-8$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots$
8379.2.a.bv	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.5744.1	None	✓	$1$	$0$	$0$	$0$	$8$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.bw	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.13068.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
8379.2.a.bx	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.725.1	None	✓	$1$	$1$	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.by	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.725.1	None	✓	$1$	$1$	$2$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
8379.2.a.bz	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.23301.1	None	✓	$1$	$0$	$2$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
8379.2.a.ca	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.23301.1	None	✓	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
8379.2.a.cb	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.368464.1	None	✓	$1$	$0$	$-3$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
8379.2.a.cc	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1244416.1	None	✓	$1$	$1$	$-3$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
8379.2.a.cd	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1244416.1	None	✓	$1$	$0$	$-3$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
8379.2.a.ce	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1240016.1	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+(\beta _{2}+\cdots)q^{8}+\cdots$
8379.2.a.cf	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.39110656.1	None	✓	$1$	$0$	$-2$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.cg	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.39110656.1	None	✓	$1$	$1$	$-2$	$0$	$4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
8379.2.a.ch	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.12730624.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
8379.2.a.ci	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.5163008.1	None	✓	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots$
8379.2.a.cj	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.5163008.1	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\beta _{5}q^{5}+\cdots$
8379.2.a.ck	$8379$	$2$	8379.a	1.a	$1$	$7$	$7$	$66.907$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}+\beta _{6}q^{5}+\cdots$
8379.2.a.cl	$8379$	$2$	8379.a	1.a	$1$	$7$	$7$	$66.907$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-2$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}-\beta _{6}q^{5}+\cdots$
8379.2.a.cm	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.$\cdots$.2	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots$
8379.2.a.cn	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.8446345216.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}-\beta _{5}q^{4}-\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots$
8379.2.a.co	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.8446345216.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}-\beta _{5}q^{4}+\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots$
8379.2.a.cp	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.$\cdots$.2	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots$
8379.2.a.cq	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$-5$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots$
8379.2.a.cr	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$5$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
8379.2.a.cs	$8379$	$2$	8379.a	1.a	$1$	$10$	$10$	$66.907$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$2$	$0$	$-16$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{9})q^{5}+\cdots$
8379.2.a.ct	$8379$	$2$	8379.a	1.a	$1$	$10$	$10$	$66.907$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$2$	$0$	$16$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots$
8379.2.a.cu	$8379$	$2$	8379.a	1.a	$1$	$12$	$12$	$66.907$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots$
8379.2.a.cv	$8379$	$2$	8379.a	1.a	$1$	$12$	$12$	$66.907$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots$
8379.2.a.cw	$8379$	$2$	8379.a	1.a	$1$	$20$	$20$	$66.907$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{10}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$
8379.2.a.cx	$8379$	$2$	8379.a	1.a	$1$	$20$	$20$	$66.907$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{10}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8379))$ into lower level spaces

Overview	Random
Universe	Knowledge

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:	\( N \)	\(=\)	\( 8379 = 3^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8379.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 76 \)
Sturm bound:			\(2240\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\), \(13\), \(17\)

\(3\)	\(7\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(28\)
\(+\)	\(+\)	\(-\)	$-$	\(36\)
\(+\)	\(-\)	\(+\)	$-$	\(36\)
\(+\)	\(-\)	\(-\)	$+$	\(24\)
\(-\)	\(+\)	\(+\)	$-$	\(46\)
\(-\)	\(+\)	\(-\)	$+$	\(42\)
\(-\)	\(-\)	\(+\)	$+$	\(45\)
\(-\)	\(-\)	\(-\)	$-$	\(51\)
Plus space			\(+\)	\(139\)
Minus space			\(-\)	\(169\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8379))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8379))\) 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	8379.2.a

Level	$8379$
Weight	$2$
Character orbit	8379.a
Rep. character	$\chi_{8379}(1,\cdot)$
Character field	$\Q$
Dimension	$308$
Newform subspaces	$76$
Sturm bound	$2240$
Trace bound	$17$