Space of modular forms of level 1305, weight 4, and Character 1305.cm

• Label: 1305.4.cm
• Level: $1305$
• Weight: $4$
• Character orbit: 1305.cm
• Rep. character: $\chi_{1305}(121,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $4320$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1305.cm (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1305, [\chi])\).

	Total	New	Old
Modular forms	6528	4320	2208
Cusp forms	6432	4320	2112
Eisenstein series	96	0	96

Trace form

4320 * q - 1440 * q^4 - 20 * q^5 + 100 * q^6 + 84 * q^8 + 36 * q^9 + 5760 * q^16 + 240 * q^20 + 210 * q^21 + 972 * q^23 + 1200 * q^24 + 9000 * q^25 - 2184 * q^27 + 46 * q^29 - 280 * q^30 - 720 * q^33 + 1120 * q^35 + 3212 * q^36 - 912 * q^38 + 952 * q^39 - 5134 * q^42 - 896 * q^44 + 1320 * q^45 - 10164 * q^48 + 18630 * q^49 + 1816 * q^51 - 1836 * q^52 - 3248 * q^53 - 1732 * q^54 + 4688 * q^57 + 594 * q^58 + 3040 * q^59 - 2040 * q^62 - 4184 * q^63 + 48780 * q^64 - 560 * q^65 - 2968 * q^69 + 224 * q^71 - 2870 * q^72 + 5720 * q^74 - 560 * q^77 - 884 * q^78 + 4480 * q^80 - 6604 * q^81 - 2808 * q^82 - 680 * q^83 + 13440 * q^84 - 868 * q^86 - 1932 * q^87 + 20440 * q^89 - 8190 * q^90 - 2520 * q^91 - 11136 * q^92 - 8072 * q^93 - 5760 * q^94 - 6290 * q^96 - 10304 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)