Space of modular forms of level 476, weight 2, and trivial character

• Label: 476.2.a
• Level: $476$
• Weight: $2$
• Character orbit: 476.a
• Rep. character: $\chi_{476}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(476))\).

	Total	New	Old
Modular forms	78	8	70
Cusp forms	67	8	59
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	\(17\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(2\)
Plus space			\(+\)	\(4\)
Minus space			\(-\)	\(4\)

Trace form

\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(476))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	17
476.2.a.a	$476$	$2$	476.a	1.a	$1$	$2$	$2$	$3.801$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-2+\beta )q^{5}+q^{7}+\cdots\)
476.2.a.b	$476$	$2$	476.a	1.a	$1$	$2$	$2$	$3.801$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
476.2.a.c	$476$	$2$	476.a	1.a	$1$	$2$	$2$	$3.801$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+4q^{11}+\cdots\)
476.2.a.d	$476$	$2$	476.a	1.a	$1$	$2$	$2$	$3.801$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(476))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)