Space of modular forms of level 790, weight 4, and Character 790.t

• Label: 790.4.t
• Level: $790$
• Weight: $4$
• Character orbit: 790.t
• Rep. character: $\chi_{790}(9,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $2880$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 790 = 2 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	790.t (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{78})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(790, [\chi])\).

	Total	New	Old
Modular forms	8736	2880	5856
Cusp forms	8544	2880	5664
Eisenstein series	192	0	192

Trace form

2880 * q - 480 * q^4 + 24 * q^6 - 1112 * q^9 + 24 * q^10 - 16 * q^11 + 224 * q^14 + 4 * q^15 + 1920 * q^16 - 144 * q^19 - 1232 * q^21 + 1152 * q^24 - 460 * q^25 - 108 * q^29 - 20 * q^30 + 4260 * q^31 - 128 * q^34 - 4508 * q^35 + 4448 * q^36 - 1856 * q^39 + 48 * q^40 - 928 * q^41 - 352 * q^44 - 110 * q^45 + 144 * q^46 - 4740 * q^49 + 1272 * q^50 - 1196 * q^51 + 240 * q^54 + 534 * q^55 - 5376 * q^56 - 4428 * q^59 + 8 * q^60 + 808 * q^61 + 15360 * q^64 - 8368 * q^65 + 7768 * q^66 - 2368 * q^69 - 3364 * q^70 + 5504 * q^71 + 4320 * q^74 + 12678 * q^75 - 14400 * q^76 + 19860 * q^79 - 13016 * q^81 + 10432 * q^84 + 7656 * q^85 + 16 * q^86 - 1976 * q^89 - 4148 * q^90 + 30088 * q^91 - 11168 * q^94 - 14268 * q^95 - 768 * q^96 + 3656 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(790, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(790, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(790, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 2}\)