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

• Label: 2904.1.t
• Level: $2904$
• Weight: $1$
• Character orbit: 2904.t
• Rep. character: $\chi_{2904}(245,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $528$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2904.t (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(528\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	136	88	48
Cusp forms	40	24	16
Eisenstein series	96	64	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q - 6 q^{4} + 2 q^{6} + 4 q^{7} - 6 q^{9} + O(q^{10}) \)

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	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2904.1.t.a	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(-1\)	\(-1\)	\(3\)	\(3\)	$1$		\(q-\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(1+\cdots)q^{5}+\cdots\)
2904.1.t.b	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(-1\)	\(1\)	\(-3\)	\(-3\)	$1$		\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(-1+\cdots)q^{5}+\cdots\)
2904.1.t.c	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(-1\)	\(1\)	\(2\)	\(2\)	$1$		\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(\zeta_{10}+\cdots)q^{5}+\cdots\)
2904.1.t.d	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(1\)	\(-1\)	\(-2\)	\(2\)	$1$		\(q+\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(-\zeta_{10}+\cdots)q^{5}+\cdots\)
2904.1.t.e	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(1\)	\(-1\)	\(3\)	\(-3\)	$1$		\(q+\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(1+\cdots)q^{5}+\cdots\)
2904.1.t.f	$2904$	$1$	2904.t	264.t	$10$	$4$	$1$	$1.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-6}) \)	None			264.1.t.a	$4$	$0$	\(1\)	\(1\)	\(-3\)	\(3\)	$1$		\(q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2904, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2904, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)