Space of modular forms of level 474, weight 2, and Character 474.i

• Label: 474.2.i
• Level: $474$
• Weight: $2$
• Character orbit: 474.i
• Rep. character: $\chi_{474}(67,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $144$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 474 = 2 \cdot 3 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	474.i (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(474, [\chi])\).

	Total	New	Old
Modular forms	1008	144	864
Cusp forms	912	144	768
Eisenstein series	96	0	96

Trace form

144 * q + 2 * q^3 - 12 * q^4 + 2 * q^6 + 8 * q^7 - 12 * q^9 + 4 * q^10 + 8 * q^11 + 2 * q^12 + 12 * q^13 + 4 * q^15 - 12 * q^16 + 8 * q^17 + 12 * q^19 + 12 * q^21 - 22 * q^22 + 24 * q^23 - 24 * q^24 - 10 * q^25 + 2 * q^27 + 8 * q^28 + 16 * q^29 + 4 * q^30 + 6 * q^31 + 8 * q^33 + 24 * q^34 + 56 * q^35 - 12 * q^36 - 4 * q^37 + 24 * q^38 + 28 * q^39 + 4 * q^40 + 40 * q^41 - 40 * q^42 + 48 * q^43 + 8 * q^44 + 16 * q^46 - 56 * q^47 + 2 * q^48 - 52 * q^49 - 88 * q^50 + 16 * q^51 + 12 * q^52 + 72 * q^53 + 2 * q^54 + 96 * q^55 + 32 * q^57 + 24 * q^58 - 16 * q^59 + 4 * q^60 + 80 * q^61 + 40 * q^62 - 18 * q^63 - 12 * q^64 - 28 * q^66 + 6 * q^67 - 44 * q^68 - 64 * q^69 - 198 * q^70 - 72 * q^71 - 224 * q^73 - 80 * q^74 - 42 * q^75 - 66 * q^76 - 224 * q^77 - 32 * q^78 + 80 * q^79 - 12 * q^81 - 4 * q^82 - 192 * q^83 - 66 * q^84 - 24 * q^85 - 24 * q^86 - 32 * q^87 + 4 * q^88 + 24 * q^89 - 22 * q^90 - 108 * q^91 - 28 * q^92 - 126 * q^93 + 28 * q^94 + 80 * q^95 + 2 * q^96 + 14 * q^97 + 64 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(474, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
474.2.i.a	$474$	$2$	474.i	79.e	$13$	$24$	$2$	$3.785$		None		✓			474.2.i.a	$2$	$0$	\(-2\)	\(-2\)	\(-10\)	\(8\)		$\mathrm{SU}(2)[C_{13}]$
474.2.i.b	$474$	$2$	474.i	79.e	$13$	$36$	$3$	$3.785$		None		✓			474.2.i.b	$2$	$0$	\(3\)	\(-3\)	\(-1\)	\(2\)		$\mathrm{SU}(2)[C_{13}]$
474.2.i.c	$474$	$2$	474.i	79.e	$13$	$36$	$3$	$3.785$		None		✓			474.2.i.c	$2$	$0$	\(3\)	\(3\)	\(12\)	\(2\)		$\mathrm{SU}(2)[C_{13}]$
474.2.i.d	$474$	$2$	474.i	79.e	$13$	$48$	$4$	$3.785$		None		✓	✓		474.2.i.d	$2$	$0$	\(-4\)	\(4\)	\(-1\)	\(-4\)		$\mathrm{SU}(2)[C_{13}]$

Decomposition of \(S_{2}^{\mathrm{old}}(474, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(474, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(158, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(237, [\chi])\)\(^{\oplus 2}\)