Space of modular forms of level 1512, weight 2, and Character 1512.c

• Label: 1512.2.c
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.c
• Rep. character: $\chi_{1512}(757,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

	Total	New	Old
Modular forms	300	96	204
Cusp forms	276	96	180
Eisenstein series	24	0	24

Trace form

96 * q - 4 * q^4 - 4 * q^10 - 20 * q^16 + 24 * q^22 - 96 * q^25 + 16 * q^28 - 16 * q^31 + 36 * q^34 + 24 * q^40 - 4 * q^46 + 96 * q^49 + 24 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^64 + 12 * q^70 - 40 * q^76 + 80 * q^79 + 12 * q^82 - 88 * q^88 + 84 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1512.2.c.a	$1512$	$2$	1512.c	8.b	$2$	$2$	$2$	$12.073$	\(\Q(\sqrt{-1}) \)	None		✓			1512.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-1)q^{2}+2 i q^{4}+2 i q^{5}+\cdots\)
1512.2.c.b	$1512$	$2$	1512.c	8.b	$2$	$2$	$2$	$12.073$	\(\Q(\sqrt{-1}) \)	None		✓			1512.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+1)q^{2}-2 i q^{4}+2 i q^{5}+\cdots\)
1512.2.c.c	$1512$	$2$	1512.c	8.b	$2$	$8$	$8$	$12.073$	8.0.3317760000.5	None		✓			1512.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
1512.2.c.d	$1512$	$2$	1512.c	8.b	$2$	$16$	$16$	$12.073$	\(\Q(\zeta_{40})\)	None		✓			1512.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{11} q^{2}-\beta_1 q^{4}+(\beta_{14}+\beta_{11}+\beta_{10})q^{5}+\cdots\)
1512.2.c.e	$1512$	$2$	1512.c	8.b	$2$	$20$	$20$	$12.073$	20.0.\(\cdots\).1	None		✓			1512.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots\)
1512.2.c.f	$1512$	$2$	1512.c	8.b	$2$	$24$	$24$	$12.073$		None		✓			1512.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$
1512.2.c.g	$1512$	$2$	1512.c	8.b	$2$	$24$	$24$	$12.073$		None		✓			1512.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)