Space of modular forms of level 414, weight 2, and Character 414.m

• Label: 414.2.m
• Level: $414$
• Weight: $2$
• Character orbit: 414.m
• Rep. character: $\chi_{414}(13,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{33})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(414, [\chi])\).

	Total	New	Old
Modular forms	1520	480	1040
Cusp forms	1360	480	880
Eisenstein series	160	0	160

Trace form

480 * q + 4 * q^3 + 24 * q^4 - 8 * q^6 + 8 * q^9 + 4 * q^11 + 4 * q^12 + 4 * q^14 + 24 * q^15 + 24 * q^16 - 16 * q^17 - 28 * q^18 - 62 * q^21 - 6 * q^23 + 4 * q^24 + 12 * q^25 + 16 * q^26 - 86 * q^27 - 16 * q^29 - 32 * q^30 - 12 * q^31 + 32 * q^33 - 16 * q^36 + 24 * q^37 + 12 * q^38 + 48 * q^39 + 4 * q^41 + 20 * q^42 - 8 * q^44 + 16 * q^45 + 12 * q^46 + 8 * q^47 - 8 * q^48 + 78 * q^49 - 8 * q^50 - 40 * q^51 + 32 * q^53 - 30 * q^54 + 24 * q^55 + 26 * q^56 - 82 * q^57 - 168 * q^59 - 6 * q^60 - 12 * q^61 - 108 * q^62 - 134 * q^63 - 48 * q^64 + 134 * q^65 - 88 * q^66 - 12 * q^67 - 80 * q^68 - 110 * q^69 - 12 * q^70 - 244 * q^71 - 52 * q^72 + 80 * q^74 - 144 * q^75 - 216 * q^77 - 50 * q^78 - 44 * q^80 + 32 * q^81 + 102 * q^83 - 6 * q^84 - 16 * q^86 - 154 * q^87 - 96 * q^89 - 28 * q^90 - 6 * q^92 - 36 * q^93 - 12 * q^94 + 12 * q^95 + 4 * q^96 + 54 * q^97 + 16 * q^98 + 84 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(414, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
414.2.m.a	$414$	$2$	414.m	207.m	$33$	$240$	$12$	$3.306$		None		✓			414.2.m.a	$4$	$0$	\(-12\)	\(0\)	\(0\)	\(-13\)		$\mathrm{SU}(2)[C_{33}]$
414.2.m.b	$414$	$2$	414.m	207.m	$33$	$240$	$12$	$3.306$		None		✓			414.2.m.b	$4$	$0$	\(12\)	\(4\)	\(0\)	\(13\)		$\mathrm{SU}(2)[C_{33}]$

Decomposition of \(S_{2}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)