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

• Label: 1305.4.bu
• Level: $1305$
• Weight: $4$
• Character orbit: 1305.bu
• Rep. character: $\chi_{1305}(199,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1332$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1305.bu (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	1356	1932
Cusp forms	3192	1332	1860
Eisenstein series	96	24	72

Trace form

1332 * q + 862 * q^4 + 19 * q^5 - 13 * q^10 + 18 * q^11 + 130 * q^14 - 3402 * q^16 - 58 * q^19 + 139 * q^20 + 599 * q^25 + 962 * q^26 + 84 * q^29 + 978 * q^31 - 338 * q^34 - 705 * q^35 + 1683 * q^40 - 760 * q^41 + 606 * q^44 - 1592 * q^46 + 7546 * q^49 - 56 * q^50 + 329 * q^55 + 1526 * q^56 - 8064 * q^59 + 2062 * q^61 + 12582 * q^64 - 720 * q^65 - 6354 * q^70 - 7374 * q^71 - 1898 * q^74 - 2130 * q^76 + 4230 * q^79 - 2164 * q^80 - 2464 * q^85 + 6276 * q^86 - 2110 * q^89 + 3030 * q^91 - 5504 * q^94 + 4407 * 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

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