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

• Label: 1305.2.ch
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.ch
• Rep. character: $\chi_{1305}(37,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $876$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.ch (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{28})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	2256	924	1332
Cusp forms	2064	876	1188
Eisenstein series	192	48	144

Trace form

876 * q + 14 * q^2 + 142 * q^4 + 14 * q^5 - 10 * q^7 + 14 * q^8 - 18 * q^10 + 20 * q^11 + 12 * q^13 + 4 * q^14 - 154 * q^16 - 6 * q^20 - 22 * q^22 + 10 * q^23 + 60 * q^25 + 84 * q^26 - 8 * q^28 + 8 * q^31 + 14 * q^32 + 56 * q^34 + 54 * q^35 - 48 * q^37 + 88 * q^38 - 42 * q^40 + 34 * q^41 - 38 * q^43 - 64 * q^44 + 20 * q^46 + 2 * q^47 - 84 * q^49 + 8 * q^50 + 150 * q^52 + 76 * q^53 - 20 * q^55 + 44 * q^56 - 156 * q^58 - 46 * q^61 - 68 * q^62 + 54 * q^64 + 24 * q^65 - 46 * q^67 + 56 * q^68 - 106 * q^70 + 28 * q^71 - 112 * q^73 + 112 * q^74 + 56 * q^77 + 20 * q^79 - 114 * q^80 + 8 * q^82 - 14 * q^83 - 4 * q^85 - 56 * q^88 + 10 * q^89 - 28 * q^91 - 26 * q^92 + 84 * q^94 - 198 * q^95 - 24 * q^97 - 68 * 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

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)