Space of modular forms of level 315, weight 8, and Character 315.j

• Label: 315.8.j
• Level: $315$
• Weight: $8$
• Character orbit: 315.j
• Rep. character: $\chi_{315}(46,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $188$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(315, [\chi])\).

	Total	New	Old
Modular forms	688	188	500
Cusp forms	656	188	468
Eisenstein series	32	0	32

Trace form

188 * q - 14 * q^2 - 5962 * q^4 - 250 * q^5 - 1058 * q^7 + 2436 * q^8 + 2000 * q^10 + 3264 * q^11 - 25072 * q^13 + 25670 * q^14 - 365118 * q^16 - 18636 * q^17 + 9516 * q^19 + 55000 * q^20 + 128 * q^22 + 24830 * q^23 - 1468750 * q^25 - 139570 * q^26 + 774298 * q^28 + 574644 * q^29 + 48168 * q^31 + 463582 * q^32 - 217992 * q^34 + 21500 * q^35 - 576804 * q^37 - 1803672 * q^38 + 384000 * q^40 + 475452 * q^41 + 19852 * q^43 - 368590 * q^44 - 147262 * q^46 - 3824676 * q^47 + 1015130 * q^49 + 437500 * q^50 + 5876164 * q^52 + 2074304 * q^53 - 1613000 * q^55 - 10264740 * q^56 - 157130 * q^58 - 1746204 * q^59 + 4254786 * q^61 + 7192080 * q^62 + 30051892 * q^64 + 795500 * q^65 - 3095186 * q^67 - 19432636 * q^68 + 1235500 * q^70 + 16728656 * q^71 - 7805816 * q^73 - 10387946 * q^74 - 42365756 * q^76 - 17089704 * q^77 - 6081156 * q^79 - 4544000 * q^80 - 2219586 * q^82 + 35670084 * q^83 + 6577000 * q^85 + 27308224 * q^86 + 2855992 * q^88 - 1919506 * q^89 + 19118824 * q^91 - 33847748 * q^92 + 46560046 * q^94 - 2370000 * q^95 + 361512 * q^97 + 61888442 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)