Space of modular forms of level 96, weight 6, and Character 96.d

• Label: 96.6.d
• Level: $96$
• Weight: $6$
• Character orbit: 96.d
• Rep. character: $\chi_{96}(49,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(96, [\chi])\).

	Total	New	Old
Modular forms	88	10	78
Cusp forms	72	10	62
Eisenstein series	16	0	16

Trace form

10 * q + 196 * q^7 - 810 * q^9 - 900 * q^15 - 404 * q^17 - 1672 * q^23 - 9366 * q^25 - 18692 * q^31 + 12168 * q^39 - 2476 * q^41 - 65256 * q^47 + 9378 * q^49 + 103424 * q^55 - 12888 * q^57 - 15876 * q^63 + 51536 * q^65 + 272232 * q^71 - 27388 * q^73 - 252308 * q^79 + 65610 * q^81 + 90828 * q^87 + 175580 * q^89 - 243184 * q^95 + 59372 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(96, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.6.d.a	$96$	$6$	96.d	8.b	$2$	$10$	$10$	$15.397$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None			✓	✓	24.6.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(196\)	$2^{40}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(20+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)