Space of modular forms of level 414, weight 4, and Character 414.p

• Label: 414.4.p
• Level: $414$
• Weight: $4$
• Character orbit: 414.p
• Rep. character: $\chi_{414}(5,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $1440$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{66})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(414, [\chi])\).

	Total	New	Old
Modular forms	4400	1440	2960
Cusp forms	4240	1440	2800
Eisenstein series	160	0	160

Trace form

1440 * q + 8 * q^3 - 288 * q^4 - 16 * q^6 + 36 * q^9 - 32 * q^12 - 1496 * q^15 + 1152 * q^16 + 40 * q^18 - 1320 * q^21 - 408 * q^23 - 32 * q^24 + 2088 * q^25 - 436 * q^27 + 636 * q^29 + 1496 * q^30 + 72 * q^31 - 3872 * q^33 + 288 * q^36 - 660 * q^39 + 300 * q^41 - 504 * q^46 + 768 * q^47 - 256 * q^48 - 1746 * q^49 + 2256 * q^50 - 3396 * q^54 - 1584 * q^55 - 5808 * q^56 - 4224 * q^57 + 1008 * q^59 - 88 * q^60 + 4180 * q^63 + 9216 * q^64 + 25872 * q^65 + 5456 * q^66 + 4082 * q^69 + 360 * q^70 + 2144 * q^72 + 10032 * q^74 + 3914 * q^75 - 7608 * q^77 + 2900 * q^78 - 12132 * q^81 - 28116 * q^83 - 3784 * q^84 - 5702 * q^87 - 1632 * q^92 + 7504 * q^93 - 1224 * q^94 - 9780 * q^95 + 128 * q^96 - 12672 * q^97 + 4620 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(414, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)