Space of modular forms of level 2, weight 46, and trivial character

• Label: 2.46.a
• Level: $2$
• Weight: $46$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $11$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 46 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(11\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{46}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	12	4	8
Cusp forms	10	4	6
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
\(+\)	\(2\)
\(-\)	\(2\)

Trace form

\( 4 q - 9904989360 q^{3} + 70368744177664 q^{4} - 105382171276200 q^{5} + 543696821919154176 q^{6} - 1661858231737805920 q^{7} + 8962376138301500039412 q^{9} + O(q^{10}) \)

Decomposition of \(S_{46}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.46.a.a	$2$	$46$	2.a	1.a	$1$	$2$	$2$	$25.651$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(-8388608\)	\(-69766206552\)	\(-45\!\cdots\!00\)	\(-95\!\cdots\!44\)		$+$	$+$	$2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b	$2$	$46$	2.a	1.a	$1$	$2$	$2$	$25.651$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(8388608\)	\(59861217192\)	\(43\!\cdots\!00\)	\(79\!\cdots\!24\)		$-$	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)

Decomposition of \(S_{46}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{46}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{46}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)