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

• Label: 1305.2.i
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.i
• Rep. character: $\chi_{1305}(436,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $224$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	368	224	144
Cusp forms	352	224	128
Eisenstein series	16	0	16

Trace form

224 * q + 4 * q^2 + 4 * q^3 - 112 * q^4 + 4 * q^6 + 4 * q^7 - 24 * q^8 + 12 * q^9 - 4 * q^11 - 4 * q^12 + 4 * q^13 - 20 * q^14 - 112 * q^16 - 8 * q^17 + 28 * q^18 + 16 * q^19 - 32 * q^21 - 12 * q^22 - 12 * q^24 - 112 * q^25 + 64 * q^26 - 8 * q^27 - 32 * q^28 - 32 * q^30 + 16 * q^31 + 68 * q^32 - 28 * q^33 - 36 * q^36 - 8 * q^37 - 44 * q^38 + 8 * q^39 + 12 * q^40 - 36 * q^41 + 16 * q^42 + 4 * q^43 - 40 * q^44 + 8 * q^45 - 24 * q^46 + 40 * q^47 + 108 * q^48 - 108 * q^49 + 4 * q^50 + 28 * q^51 + 16 * q^52 + 48 * q^53 - 16 * q^54 + 12 * q^56 - 12 * q^57 + 12 * q^59 + 28 * q^60 + 28 * q^61 - 72 * q^63 + 200 * q^64 + 64 * q^66 + 16 * q^67 - 52 * q^68 - 112 * q^69 - 32 * q^71 - 80 * q^72 + 16 * q^73 + 4 * q^75 - 8 * q^76 - 16 * q^77 - 72 * q^78 + 4 * q^79 + 32 * q^80 + 92 * q^81 + 24 * q^82 - 32 * q^83 + 152 * q^84 + 68 * q^86 - 36 * q^88 - 48 * q^89 - 88 * q^91 + 72 * q^92 + 64 * q^93 + 24 * q^95 - 140 * q^96 - 32 * q^97 - 136 * q^98 + 40 * 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.

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

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)