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

• Label: 315.8.cg
• Level: $315$
• Weight: $8$
• Character orbit: 315.cg
• Rep. character: $\chi_{315}(157,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1328$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.cg (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	1360	1360	0
Cusp forms	1328	1328	0
Eisenstein series	32	32	0

Trace form

1328 * q + 2 * q^2 - 6 * q^3 - 2 * q^7 + 496 * q^8 - 12 * q^10 + 11808 * q^11 - 6 * q^12 - 12602 * q^15 + 2621444 * q^16 - 81678 * q^17 - 101762 * q^18 - 196608 * q^20 + 38436 * q^21 - 516 * q^22 - 4596 * q^23 - 4 * q^25 - 24 * q^26 - 154188 * q^27 + 33016 * q^28 + 725056 * q^30 - 12 * q^31 + 174198 * q^32 - 887016 * q^33 - 226844 * q^35 - 807440 * q^36 - 4 * q^37 - 1422804 * q^41 + 68786 * q^42 - 4 * q^43 - 2585508 * q^45 + 602008 * q^46 - 6 * q^47 - 85950 * q^48 + 2954852 * q^50 - 1728892 * q^51 + 181456 * q^53 + 7528160 * q^56 + 2759768 * q^57 - 1385540 * q^58 - 5333950 * q^60 - 7730904 * q^61 - 10862154 * q^63 + 6322346 * q^65 - 3359244 * q^66 + 2 * q^67 - 625002 * q^70 + 12089024 * q^71 + 25285546 * q^72 - 12 * q^73 - 6 * q^75 - 196608 * q^76 + 4050038 * q^77 + 16950730 * q^78 + 98292 * q^80 - 15278596 * q^81 - 780 * q^82 + 49131012 * q^83 - 4 * q^85 + 22333328 * q^86 - 13128 * q^87 - 8520708 * q^88 + 36049824 * q^90 - 16 * q^91 + 506620 * q^92 - 32374724 * q^93 - 30512210 * q^95 + 79822836 * q^96 + 105415500 * 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.