Space of modular forms of level 1305, weight 2, and Character 1305.cm

• Label: 1305.2.cm
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.cm
• Rep. character: $\chi_{1305}(121,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1440$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.cm (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	2208	1440	768
Cusp forms	2112	1440	672
Eisenstein series	96	0	96

Trace form

1440 * q - 120 * q^4 + 4 * q^5 - 32 * q^6 + 84 * q^8 - 12 * q^9 + 120 * q^16 - 12 * q^20 - 54 * q^23 - 78 * q^24 + 120 * q^25 + 84 * q^27 + 4 * q^29 - 4 * q^30 - 90 * q^33 - 32 * q^35 + 56 * q^36 + 24 * q^38 + 70 * q^39 + 134 * q^42 + 112 * q^44 + 24 * q^45 - 84 * q^48 + 90 * q^49 + 28 * q^51 + 36 * q^52 + 64 * q^53 + 68 * q^54 - 112 * q^57 - 18 * q^58 + 4 * q^59 - 312 * q^62 - 104 * q^63 + 60 * q^64 - 26 * q^65 + 56 * q^69 - 64 * q^71 + 70 * q^72 + 20 * q^74 - 140 * q^77 - 68 * q^78 - 56 * q^80 + 92 * q^81 - 72 * q^82 - 20 * q^83 - 168 * q^84 + 44 * q^86 - 60 * q^87 + 28 * q^89 + 126 * q^90 + 60 * q^91 + 168 * q^92 + 148 * q^93 - 66 * q^94 - 110 * q^96 - 224 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

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