Space of modular forms of level 476, weight 2, and Character 476.i

• Label: 476.2.i
• Level: $476$
• Weight: $2$
• Character orbit: 476.i
• Rep. character: $\chi_{476}(137,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(476, [\chi])\).

	Total	New	Old
Modular forms	156	20	136
Cusp forms	132	20	112
Eisenstein series	24	0	24

Trace form

20 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 12 * q^9 - 4 * q^11 - 8 * q^15 + 4 * q^17 - 6 * q^19 - 8 * q^21 + 4 * q^23 - 14 * q^25 - 16 * q^27 + 16 * q^29 - 18 * q^31 + 2 * q^33 + 10 * q^35 - 2 * q^37 + 12 * q^39 - 28 * q^41 + 44 * q^43 - 28 * q^45 - 10 * q^47 + 8 * q^49 + 4 * q^53 + 4 * q^55 + 16 * q^57 + 10 * q^59 + 16 * q^61 - 34 * q^63 - 6 * q^65 + 40 * q^69 + 20 * q^71 + 4 * q^73 + 40 * q^75 - 30 * q^77 - 36 * q^79 + 2 * q^81 + 24 * q^83 - 42 * q^87 + 8 * q^89 + 4 * q^91 - 22 * q^93 + 12 * q^95 - 12 * q^97 + 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(476, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
476.2.i.a	$476$	$2$	476.i	7.c	$3$	$2$	$1$	$3.801$	\(\Q(\sqrt{-3}) \)	None		✓			476.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
476.2.i.b	$476$	$2$	476.i	7.c	$3$	$2$	$1$	$3.801$	\(\Q(\sqrt{-3}) \)	None		✓			476.2.i.b	$2$	$0$	\(0\)	\(1\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
476.2.i.c	$476$	$2$	476.i	7.c	$3$	$2$	$1$	$3.801$	\(\Q(\sqrt{-3}) \)	None		✓			476.2.i.c	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
476.2.i.d	$476$	$2$	476.i	7.c	$3$	$6$	$3$	$3.801$	6.0.1783323.2	None		✓			476.2.i.d	$2$	$0$	\(0\)	\(1\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
476.2.i.e	$476$	$2$	476.i	7.c	$3$	$8$	$4$	$3.801$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓		476.2.i.e	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(476, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)