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

• Label: 1305.2.bc
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.bc
• Rep. character: $\chi_{1305}(136,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $300$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.bc (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	1128	300	828
Cusp forms	1032	300	732
Eisenstein series	96	0	96

Trace form

300 * q - 4 * q^2 - 54 * q^4 + 2 * q^5 - 4 * q^7 - 42 * q^8 + 24 * q^11 - 4 * q^13 - 8 * q^14 - 34 * q^16 - 12 * q^17 - 4 * q^19 + 6 * q^20 + 34 * q^22 - 24 * q^23 - 50 * q^25 - 16 * q^26 - 48 * q^28 + 12 * q^29 + 18 * q^31 + 102 * q^32 + 36 * q^34 + 4 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^41 + 16 * q^43 - 6 * q^44 + 44 * q^46 + 72 * q^47 - 80 * q^49 - 4 * q^50 - 116 * q^52 - 28 * q^53 - 20 * q^55 + 40 * q^56 + 28 * q^58 + 52 * q^59 - 68 * q^61 + 154 * q^62 + 76 * q^64 - 2 * q^65 - 32 * q^67 - 4 * q^68 + 12 * q^70 + 78 * q^71 - 12 * q^73 - 114 * q^74 - 104 * q^76 - 78 * q^77 + 12 * q^79 - 2 * q^80 - 18 * q^82 + 4 * q^83 - 16 * q^85 - 64 * q^86 - 76 * q^88 - 112 * q^89 + 34 * q^91 - 118 * q^92 - 14 * q^94 - 8 * q^95 - 12 * q^97 + 6 * 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

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)