Space of modular forms of level 418, weight 2, and Character 418.v

• Label: 418.2.v
• Level: $418$
• Weight: $2$
• Character orbit: 418.v
• Rep. character: $\chi_{418}(13,\cdot)$
• Character field: $\Q(\zeta_{90})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{90})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(418, [\chi])\).

	Total	New	Old
Modular forms	1536	480	1056
Cusp forms	1344	480	864
Eisenstein series	192	0	192

Trace form

480 * q + 6 * q^3 - 15 * q^6 + 30 * q^7 + 6 * q^9 - 6 * q^11 - 36 * q^14 - 48 * q^15 + 30 * q^17 + 24 * q^20 - 24 * q^22 + 15 * q^24 - 36 * q^25 - 12 * q^26 - 18 * q^27 + 30 * q^29 + 18 * q^31 + 18 * q^33 - 48 * q^34 - 9 * q^36 - 12 * q^38 + 30 * q^41 - 12 * q^42 - 30 * q^44 + 96 * q^45 - 108 * q^47 + 12 * q^48 - 162 * q^49 - 30 * q^51 + 42 * q^53 - 198 * q^55 - 120 * q^57 - 48 * q^58 + 183 * q^59 + 36 * q^60 - 90 * q^62 + 60 * q^64 - 147 * q^66 - 18 * q^67 - 30 * q^68 - 108 * q^69 + 48 * q^70 - 54 * q^71 + 144 * q^77 - 144 * q^81 + 75 * q^82 - 300 * q^85 + 6 * q^86 + 36 * q^89 - 120 * q^90 - 6 * q^91 + 294 * q^93 - 33 * q^97 - 237 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(418, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
418.2.v.a	$418$	$2$	418.v	209.w	$90$	$240$	$10$	$3.338$		None		✓			418.2.v.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(33\)		$\mathrm{SU}(2)[C_{90}]$
418.2.v.b	$418$	$2$	418.v	209.w	$90$	$240$	$10$	$3.338$		None		✓			418.2.v.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{90}]$

Decomposition of \(S_{2}^{\mathrm{old}}(418, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(418, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)