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

• Label: 1305.2.co
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.co
• Rep. character: $\chi_{1305}(4,\cdot)$
• 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.co (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 + 162 * q^4 - 5 * q^5 - 8 * q^6 - 32 * q^9 - 28 * q^10 - 14 * q^11 - 14 * q^14 - 14 * q^15 + 162 * q^16 - 56 * q^19 - 3 * q^20 - 28 * q^21 + 6 * q^24 - 5 * q^25 - 56 * q^26 - 14 * q^29 - 48 * q^30 - 14 * q^31 - 30 * q^34 + 24 * q^35 - 88 * q^36 - 42 * q^39 - 7 * q^40 + 56 * q^44 - 6 * q^45 - 192 * q^49 - 7 * q^50 - 72 * q^51 + 56 * q^55 + 14 * q^56 - 312 * q^59 + 7 * q^60 - 14 * q^61 - 384 * q^64 + 29 * q^65 - 28 * q^66 + 28 * q^69 - 180 * q^71 + 26 * q^74 - 14 * q^76 - 14 * q^79 + 440 * q^80 - 152 * q^81 - 14 * q^84 - 42 * q^85 - 324 * q^86 - 56 * q^89 + 56 * q^90 - 44 * q^91 - 56 * q^94 + 49 * q^95 - 280 * q^96

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

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