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

• Label: 315.8.i
• Level: $315$
• Weight: $8$
• Character orbit: 315.i
• Rep. character: $\chi_{315}(106,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $336$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
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	680	336	344
Cusp forms	664	336	328
Eisenstein series	16	0	16

Trace form

336 * q - 32 * q^2 + 52 * q^3 - 10752 * q^4 - 1724 * q^6 + 22680 * q^8 + 7856 * q^9 - 3678 * q^11 + 28104 * q^12 - 1750 * q^15 - 688128 * q^16 - 143832 * q^17 - 204908 * q^18 + 8376 * q^19 - 28126 * q^21 - 141024 * q^22 - 292008 * q^23 - 342896 * q^24 - 2625000 * q^25 + 797456 * q^26 + 304984 * q^27 - 262376 * q^29 - 956000 * q^30 - 1582592 * q^32 + 781624 * q^33 - 35532 * q^34 + 686000 * q^35 + 1537228 * q^36 - 955552 * q^38 - 970314 * q^39 + 799500 * q^40 - 2152044 * q^41 + 1441284 * q^43 + 5391552 * q^44 + 701000 * q^45 - 2164488 * q^46 - 975432 * q^47 - 6333656 * q^48 - 19765032 * q^49 - 500000 * q^50 + 862294 * q^51 + 4487148 * q^52 + 6859264 * q^53 - 5523184 * q^54 - 15342456 * q^57 - 5179068 * q^58 + 8368260 * q^59 - 448000 * q^60 + 26920584 * q^62 + 2225384 * q^63 + 113910000 * q^64 - 5127250 * q^65 + 5781452 * q^66 + 4338276 * q^67 + 15499900 * q^68 + 5173524 * q^69 - 15462160 * q^71 + 24752444 * q^72 - 19216584 * q^73 - 1630340 * q^74 + 812500 * q^75 - 8105892 * q^76 - 7304528 * q^77 - 8639136 * q^78 + 2735922 * q^79 - 23404000 * q^80 - 35818496 * q^81 - 451848 * q^82 + 40548220 * q^83 + 30948204 * q^84 - 1317750 * q^85 + 63027480 * q^86 + 27905316 * q^87 - 27076608 * q^88 - 113019800 * q^89 - 20192000 * q^90 + 8474844 * q^91 + 10122008 * q^92 - 4082088 * q^93 + 16838676 * q^94 - 16797000 * q^95 + 88082324 * q^96 - 31778172 * q^97 + 7529536 * q^98 + 9769000 * q^99

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

\( S_{8}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)