Space of modular forms of level 2904, weight 1, and Character 2904.n

• Label: 2904.1.n
• Level: $2904$
• Weight: $1$
• Character orbit: 2904.n
• Rep. character: $\chi_{2904}(485,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $528$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2904.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(528\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2904, [\chi])\).

	Total	New	Old
Modular forms	32	26	6
Cusp forms	8	8	0
Eisenstein series	24	18	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 8 q^{4} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2904, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2904.1.n.a	$2904$	$1$	2904.n	24.h	$2$	$2$	$2$	$1.449$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(-2\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q-q^{2}-q^{3}+q^{4}+(1-\beta )q^{5}+q^{6}+\cdots\)
2904.1.n.b	$2904$	$1$	2904.n	24.h	$2$	$2$	$2$	$1.449$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(-2\)	\(2\)	\(-1\)	\(1\)	$1$		\(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
2904.1.n.c	$2904$	$1$	2904.n	24.h	$2$	$2$	$2$	$1.449$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(2\)	\(-2\)	\(1\)	\(1\)	$1$		\(q+q^{2}-q^{3}+q^{4}+(1-\beta )q^{5}-q^{6}+\cdots\)
2904.1.n.d	$2904$	$1$	2904.n	24.h	$2$	$2$	$2$	$1.449$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(2\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)