Space of modular forms of level 315, weight 4, and Character 315.bh

• Label: 315.4.bh
• Level: $315$
• Weight: $4$
• Character orbit: 315.bh
• Rep. character: $\chi_{315}(169,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	296	216	80
Cusp forms	280	216	64
Eisenstein series	16	0	16

Trace form

216 * q + 432 * q^4 - 8 * q^5 - 32 * q^9 - 180 * q^11 + 112 * q^14 - 56 * q^15 - 1728 * q^16 + 282 * q^20 - 56 * q^21 - 396 * q^24 - 144 * q^25 + 544 * q^26 + 904 * q^29 + 380 * q^30 + 72 * q^31 - 396 * q^34 - 2220 * q^36 - 260 * q^39 - 256 * q^41 - 6016 * q^44 - 1908 * q^45 + 72 * q^46 + 5292 * q^49 + 70 * q^50 - 3148 * q^51 + 3876 * q^54 - 792 * q^55 - 1344 * q^56 + 1568 * q^59 + 4608 * q^60 - 15192 * q^64 - 1616 * q^65 + 9256 * q^66 - 4280 * q^69 + 9264 * q^71 + 7796 * q^74 - 6204 * q^75 - 1116 * q^76 + 468 * q^79 + 5144 * q^80 - 688 * q^81 - 1792 * q^84 + 1656 * q^85 - 4828 * q^86 + 640 * q^89 - 8692 * q^90 + 504 * q^91 + 3312 * q^94 + 1340 * q^95 - 14148 * q^96 + 1584 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)