Space of modular forms of level 1305, weight 4, and Character 1305.br

• Label: 1305.4.br
• Level: $1305$
• Weight: $4$
• Character orbit: 1305.br
• Rep. character: $\chi_{1305}(64,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1344$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1305.br (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1305, [\chi])\).

	Total	New	Old
Modular forms	3288	1368	1920
Cusp forms	3192	1344	1848
Eisenstein series	96	24	72

Trace form

1344 * q - 906 * q^4 - 3 * q^5 - 7 * q^10 + 14 * q^11 + 14 * q^14 - 3562 * q^16 - 14 * q^19 + 275 * q^20 - 775 * q^25 + 266 * q^26 - 342 * q^29 + 294 * q^31 - 126 * q^34 + 943 * q^35 + 833 * q^40 - 434 * q^44 + 10408 * q^49 - 434 * q^50 - 1435 * q^55 - 686 * q^56 + 7616 * q^59 - 2030 * q^61 - 14826 * q^64 + 2355 * q^65 - 5038 * q^71 - 6642 * q^74 - 2702 * q^76 - 14 * q^79 - 4262 * q^80 - 5418 * q^85 + 12508 * q^86 + 14 * q^89 + 3726 * q^91 + 9372 * q^94 - 5593 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

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