Space of modular forms of level 477, weight 2, and Character 477.c

• Label: 477.2.c
• Level: $477$
• Weight: $2$
• Character orbit: 477.c
• Rep. character: $\chi_{477}(370,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 477 = 3^{2} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	477.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(477, [\chi])\).

	Total	New	Old
Modular forms	58	24	34
Cusp forms	50	22	28
Eisenstein series	8	2	6

Trace form

\( 22 q - 30 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(477, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
477.2.c.a	$477$	$2$	477.c	53.b	$2$	$4$	$4$	$3.809$	4.0.7168.1	None					53.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
477.2.c.b	$477$	$2$	477.c	53.b	$2$	$8$	$8$	$3.809$	8.0.\(\cdots\).3	None					159.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
477.2.c.c	$477$	$2$	477.c	53.b	$2$	$10$	$10$	$3.809$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	\(\Q(\sqrt{-159}) \)		✓	✓		477.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{6}q^{5}-\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(477, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(477, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(159, [\chi])\)\(^{\oplus 2}\)