Space of modular forms of level 315, weight 10, and Character 315.j

• Label: 315.10.j
• Level: $315$
• Weight: $10$
• Character orbit: 315.j
• Rep. character: $\chi_{315}(46,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $240$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	880	240	640
Cusp forms	848	240	608
Eisenstein series	32	0	32

Trace form

240 * q + 34 * q^2 - 30890 * q^4 + 1250 * q^5 + 1140 * q^7 - 67932 * q^8 - 20000 * q^10 - 109734 * q^11 - 441856 * q^13 - 25882 * q^14 - 8276574 * q^16 + 609420 * q^17 + 1006502 * q^19 - 2825000 * q^20 + 2965664 * q^22 + 3432560 * q^23 - 46875000 * q^25 - 5493394 * q^26 + 2521562 * q^28 + 4462356 * q^29 - 9031840 * q^31 + 10360126 * q^32 - 69029192 * q^34 + 7591250 * q^35 + 41792404 * q^37 + 8525256 * q^38 - 15360000 * q^40 + 40581240 * q^41 + 4775216 * q^43 - 96230206 * q^44 + 25849954 * q^46 + 151776816 * q^47 - 86110330 * q^49 - 26562500 * q^50 + 174437316 * q^52 - 11557588 * q^53 + 68740000 * q^55 + 620709468 * q^56 - 212791290 * q^58 + 95453604 * q^59 - 465417750 * q^61 + 29977200 * q^62 + 4404608308 * q^64 + 108773750 * q^65 + 142855192 * q^67 + 1156434356 * q^68 - 795422500 * q^70 - 1276363792 * q^71 - 423304604 * q^73 - 836607962 * q^74 - 279007132 * q^76 + 3028751784 * q^77 + 237383720 * q^79 + 805120000 * q^80 - 2456701298 * q^82 - 876351216 * q^83 - 279520000 * q^85 - 2460256928 * q^86 + 654649928 * q^88 + 1448769182 * q^89 - 3398220028 * q^91 - 8402830052 * q^92 - 3587080178 * q^94 - 284437500 * q^95 - 6241284752 * q^97 + 4899763562 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)