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

• Label: 414.4.i
• Level: $414$
• Weight: $4$
• Character orbit: 414.i
• Rep. character: $\chi_{414}(55,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $300$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(288\)

Dimensions

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

	Total	New	Old
Modular forms	2240	300	1940
Cusp forms	2080	300	1780
Eisenstein series	160	0	160

Trace form

300 * q - 120 * q^4 + 22 * q^5 - 8 * q^7 + 20 * q^10 - 10 * q^11 - 80 * q^13 + 24 * q^14 - 480 * q^16 + 12 * q^17 - 162 * q^19 - 264 * q^20 - 584 * q^22 - 800 * q^23 - 1142 * q^25 - 252 * q^26 + 144 * q^28 + 292 * q^29 + 824 * q^31 - 248 * q^34 + 886 * q^35 - 1386 * q^37 - 20 * q^38 + 80 * q^40 - 274 * q^41 + 2034 * q^43 - 40 * q^44 + 244 * q^46 - 1928 * q^47 - 3880 * q^49 + 776 * q^50 - 320 * q^52 - 1172 * q^53 - 7564 * q^55 - 1840 * q^56 - 2240 * q^58 - 26 * q^59 + 594 * q^61 + 1940 * q^62 - 1920 * q^64 + 6240 * q^65 - 114 * q^67 + 2336 * q^68 + 4880 * q^70 + 5968 * q^71 - 268 * q^73 + 2108 * q^74 + 232 * q^76 + 224 * q^77 - 3206 * q^79 - 1056 * q^80 - 4496 * q^82 - 11516 * q^83 - 11162 * q^85 - 6432 * q^86 - 400 * q^88 - 2386 * q^89 - 2144 * q^91 + 672 * q^92 + 432 * q^94 + 4744 * q^95 + 10846 * q^97 + 6760 * q^98

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

\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)