Space of modular forms of level 91, weight 8, and trivial character

• Label: 91.8.a
• Level: $91$
• Weight: $8$
• Character orbit: 91.a
• Rep. character: $\chi_{91}(1,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $5$
• Sturm bound: $74$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(74\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(91))\).

	Total	New	Old
Modular forms	66	42	24
Cusp forms	62	42	20
Eisenstein series	4	0	4

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

\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(11\)
\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	$-$	\(10\)
\(-\)	\(-\)	$+$	\(12\)
Plus space		\(+\)	\(23\)
Minus space		\(-\)	\(19\)

Trace form

\( 42 q + 2 q^{2} - 104 q^{3} + 2766 q^{4} + 284 q^{5} + 1160 q^{6} + 686 q^{7} + 1854 q^{8} + 28226 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(91))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	13
91.8.a.a	$91$	$8$	91.a	1.a	$1$	$1$	$1$	$28.427$	\(\Q\)	None	✓	$1$	$0$	\(22\)	\(21\)	\(140\)	\(-343\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+22q^{2}+21q^{3}+356q^{4}+140q^{5}+\cdots\)
91.8.a.b	$91$	$8$	91.a	1.a	$1$	$9$	$9$	$28.427$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(-26\)	\(-181\)	\(-3087\)		$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-3+\beta _{2})q^{3}+(43+\cdots)q^{4}+\cdots\)
91.8.a.c	$91$	$8$	91.a	1.a	$1$	$10$	$10$	$28.427$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-18\)	\(-80\)	\(-927\)	\(3430\)		$-$	$+$	$-$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-8-\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.8.a.d	$91$	$8$	91.a	1.a	$1$	$10$	$10$	$28.427$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(-101\)	\(226\)	\(-3430\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-10-\beta _{1}-\beta _{3})q^{3}+(6^{2}+\cdots)q^{4}+\cdots\)
91.8.a.e	$91$	$8$	91.a	1.a	$1$	$12$	$12$	$28.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(82\)	\(1026\)	\(4116\)		$-$	$-$	$+$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(82+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(91))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(91)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)