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

• Label: 2624.1.h
• Level: $2624$
• Weight: $1$
• Character orbit: 2624.h
• Rep. character: $\chi_{2624}(2623,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $3$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2624 = 2^{6} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2624.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	46	9	37
Cusp forms	34	7	27
Eisenstein series	12	2	10

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q + 2 q^{5} + 5 q^{9} + O(q^{10}) \)

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.h.a	$2624$	$1$	2624.h	164.d	$2$	$1$	$1$	$1.310$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \)	\(\Q(\sqrt{41}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots\)
2624.1.h.b	$2624$	$1$	2624.h	164.d	$2$	$2$	$2$	$1.310$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-41}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
2624.1.h.c	$2624$	$1$	2624.h	164.d	$2$	$4$	$4$	$1.310$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-41}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2624, [\chi]) \cong \)