Space of modular forms of level 1476, weight 1, and Character 1476.ba

• Label: 1476.1.ba
• Level: $1476$
• Weight: $1$
• Character orbit: 1476.ba
• Rep. character: $\chi_{1476}(379,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $252$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1476.ba (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(252\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1476, [\chi])\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	16	4	12
Eisenstein series	32	8	24

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

\( 4 q + q^{2} - q^{4} + 2 q^{5} + q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1476, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1476.1.ba.a	$1476$	$1$	1476.ba	164.j	$10$	$4$	$1$	$0.737$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(492, [\chi])\)\(^{\oplus 2}\)