Space of modular forms of level 2, weight 88, and trivial character

• Label: 2.88.a
• Level: $2$
• Weight: $88$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{88}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	23	7	16
Cusp forms	21	7	14
Eisenstein series	2	0	2

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

\(2\)	Dim
\(+\)	\(4\)
\(-\)	\(3\)

Trace form

\( 7 q - 8796093022208 q^{2} + 80974745693182072212 q^{3} + 541598767187353870268366848 q^{4} - 2920508893103043329722952304510 q^{5} - 6381576261198159352072644593713152 q^{6} + 5685733200018651170793947092255103816 q^{7} - 680564733841876926926749214863536422912 q^{8} + 879093243194986986690731015132457684762339 q^{9} + O(q^{10}) \)

Decomposition of \(S_{88}^{\mathrm{new}}(\Gamma_0(2))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
2.88.a.a	$2$	$88$	2.a	1.a	$1$	$3$	$3$	$95.867$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(26\!\cdots\!24\)	\(-32\!\cdots\!16\)	\(11\!\cdots\!50\)	\(-28\!\cdots\!88\)		$-$	$-$	$2^{23}\cdot 3^{9}\cdot 5^{3}\cdot 7\cdot 11\cdot 29$	$\mathrm{SU}(2)$	\(q+2^{43}q^{2}+(-107421079853628369972+\cdots)q^{3}+\cdots\)
2.88.a.b	$2$	$88$	2.a	1.a	$1$	$4$	$4$	$95.867$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-35\!\cdots\!32\)	\(40\!\cdots\!28\)	\(-40\!\cdots\!60\)	\(85\!\cdots\!04\)		$+$	$+$	$2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29$	$\mathrm{SU}(2)$	\(q-2^{43}q^{2}+(100809496313516795532+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{88}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{88}^{\mathrm{old}}(\Gamma_0(2)) \simeq \) \(S_{88}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)