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

• Label: 1305.2.cj
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.cj
• Rep. character: $\chi_{1305}(49,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $2112$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.cj (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1305 \)
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	2208	0
Cusp forms	2112	2112	0
Eisenstein series	96	96	0

Trace form

2112 * q - 182 * q^4 - 5 * q^5 - 32 * q^6 - 24 * q^9 - 12 * q^10 - 6 * q^11 + 2 * q^14 - 10 * q^15 + 146 * q^16 - 40 * q^19 - 39 * q^20 - 24 * q^21 - 138 * q^24 - 5 * q^25 - 24 * q^26 - 14 * q^29 - 64 * q^30 - 10 * q^31 + 10 * q^34 + 24 * q^35 - 104 * q^36 - 50 * q^39 + q^40 - 20 * q^41 - 136 * q^44 - 18 * q^45 - 104 * q^46 - 132 * q^49 + 3 * q^50 + 40 * q^51 + 16 * q^54 + 20 * q^55 - 38 * q^56 + 264 * q^59 - 87 * q^60 + 2 * q^61 + 240 * q^64 - 11 * q^65 - 160 * q^66 - 44 * q^69 - 38 * q^70 - 244 * q^71 + 10 * q^74 + 126 * q^75 + 22 * q^76 - 46 * q^79 - 272 * q^80 - 88 * q^81 + 18 * q^84 - 4 * q^85 - 220 * q^86 + 16 * q^89 - 8 * q^90 + 76 * q^91 + 36 * q^94 + 121 * q^95 + 24 * q^96 - 140 * q^99

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

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