Space of modular forms of level 960, weight 2, and Character 960.bc

• Label: 960.2.bc
• Level: $960$
• Weight: $2$
• Character orbit: 960.bc
• Rep. character: $\chi_{960}(367,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	$N$	$=$	$960 = 2^{6} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	960.bc (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$80$
Character field:			$\Q(i)$
Newform subspaces:			$6$
Sturm bound:			$384$
Trace bound:			$11$
Distinguishing $T_p$:			$7$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(960, [\chi])$.

	Total	New	Old
Modular forms	416	48	368
Cusp forms	352	48	304
Eisenstein series	64	0	64

Trace form

$48 q - 48 q^{9} + 8 q^{19} + 24 q^{35} - 32 q^{43} - 48 q^{47} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 48 q^{67} - 16 q^{69} + 64 q^{71} - 16 q^{73} + 16 q^{75} + 48 q^{81} + 32 q^{91} - 80 q^{95}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(960, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.2.bc.a	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	$\Q(\sqrt{-1})$	None					240.2.y.b	$2$	$0$	$0$	$0$	$-4$	$-6$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{3}+(i-2)q^{5}+(-3 i-3)q^{7}+\cdots$
960.2.bc.b	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	$\Q(\sqrt{-1})$	None					240.2.y.c	$2$	$1$	$0$	$0$	$-4$	$-6$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{3}+(-i-2)q^{5}+(-3 i-3)q^{7}+\cdots$
960.2.bc.c	$960$	$2$	960.bc	80.j	$4$	$2$	$1$	$7.666$	$\Q(\sqrt{-1})$	None					240.2.y.a	$2$	$1$	$0$	$0$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{3}+(i-2)q^{5}+(i+1)q^{7}-q^{9}+\cdots$
960.2.bc.d	$960$	$2$	960.bc	80.j	$4$	$6$	$3$	$7.666$	6.0.399424.1	None					240.2.y.d	$2$	$0$	$0$	$0$	$12$	$2$	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(2-\beta _{1})q^{5}-\beta _{5}q^{7}-q^{9}+\cdots$
960.2.bc.e	$960$	$2$	960.bc	80.j	$4$	$16$	$8$	$7.666$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					240.2.y.e	$2$	$0$	$0$	$0$	$-8$	$4$	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{3}+(-1+\beta _{10}+\beta _{11})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
960.2.bc.f	$960$	$2$	960.bc	80.j	$4$	$20$	$10$	$7.666$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None			✓		240.2.y.f	$2$	$0$	$0$	$0$	$8$	$4$	$2^{17}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{3}-\beta _{12}q^{5}+\beta _{1}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(960, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(960, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(80, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(240, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(320, [\chi])$$^{\oplus 2}$