Space of modular forms of level 2624, weight 1, and Character 2624.bt

• Label: 2624.1.bt
• Level: $2624$
• Weight: $1$
• Character orbit: 2624.bt
• Rep. character: $\chi_{2624}(447,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2624 = 2^{6} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2624.bt (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2624, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	24	4	20
Eisenstein series	48	8	40

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2624, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2624.1.bt.a	$2624$	$1$	2624.bt	164.j	$10$	$4$	$1$	$1.310$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{5}+q^{9}+(-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2624, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2624, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1312, [\chi])\)\(^{\oplus 2}\)