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

• Label: 315.8.l
• Level: $315$
• Weight: $8$
• Character orbit: 315.l
• Rep. character: $\chi_{315}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $448$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
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	448	232
Cusp forms	664	448	216
Eisenstein series	16	0	16

Trace form

448 * q + 28672 * q^4 + 500 * q^5 - 928 * q^6 + 166 * q^7 + 2082 * q^9 + 2954 * q^11 - 9230 * q^12 - 3694 * q^13 + 20046 * q^14 + 1750 * q^15 + 1835008 * q^16 + 78608 * q^17 + 12342 * q^18 + 44684 * q^19 + 96000 * q^20 - 24550 * q^21 - 46878 * q^23 + 120844 * q^24 - 3500000 * q^25 - 52928 * q^26 + 125502 * q^27 + 42496 * q^28 + 46250 * q^29 + 26000 * q^30 - 430096 * q^31 + 2136920 * q^32 + 434756 * q^33 + 1998840 * q^36 + 12434 * q^37 + 1148068 * q^38 - 560422 * q^39 - 1023362 * q^41 + 2963784 * q^42 + 96104 * q^43 + 706306 * q^44 - 756750 * q^45 + 301008 * q^46 - 5535832 * q^47 - 9937012 * q^48 + 32680 * q^49 - 753160 * q^51 - 945664 * q^52 + 1704240 * q^53 - 2849142 * q^54 + 1070076 * q^56 + 574682 * q^57 - 811420 * q^59 - 3811500 * q^60 + 8315816 * q^61 - 26463048 * q^62 + 5681132 * q^63 + 117440512 * q^64 - 1466500 * q^65 - 6811736 * q^66 - 5007436 * q^67 + 14031806 * q^68 + 25802760 * q^69 - 1164000 * q^70 + 25622832 * q^71 + 8193242 * q^72 - 11731804 * q^73 + 10517768 * q^74 + 11439104 * q^76 + 22826230 * q^77 - 20513240 * q^78 - 430672 * q^79 + 14336000 * q^80 + 13034474 * q^81 + 32228716 * q^83 - 21737796 * q^84 + 1317750 * q^85 + 22544858 * q^86 - 32263198 * q^87 - 6662642 * q^89 + 3966750 * q^90 + 3448178 * q^91 - 34516540 * q^92 + 4517718 * q^93 + 23170368 * q^94 + 33753142 * q^96 + 6614834 * q^97 + 43594730 * q^98 + 9411390 * 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

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