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

• Label: 315.8.bs
• Level: $315$
• Weight: $8$
• Character orbit: 315.bs
• Rep. character: $\chi_{315}(52,\cdot)$
• 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.bs (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 - 4 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7 + 496 * q^8 - 12 * q^10 - 5904 * q^11 - 774 * q^12 - 12602 * q^15 - 5242888 * q^16 - 81678 * q^17 + 51646 * q^18 + 196608 * q^20 + 27888 * q^21 - 516 * q^22 + 2298 * q^23 + 2 * q^25 - 24 * q^26 + 154188 * q^27 + 33016 * q^28 - 1048634 * q^30 - 348396 * q^32 - 6 * q^33 - 226844 * q^35 - 807440 * q^36 - 4 * q^37 - 6 * q^38 - 6 * q^40 + 1422804 * q^41 + 54896 * q^42 - 4 * q^43 - 2389014 * q^45 + 602008 * q^46 + 85950 * q^48 + 2954852 * q^50 + 2875568 * q^51 + 196602 * q^52 + 181456 * q^53 - 4752844 * q^56 + 2759768 * q^57 + 692770 * q^58 - 1139134 * q^60 - 3572862 * q^63 - 12644692 * q^65 - 12 * q^66 - 4 * q^67 + 20908026 * q^68 + 312498 * q^70 + 12089024 * q^71 - 8827994 * q^72 - 12 * q^73 + 18647946 * q^75 + 196608 * q^76 - 9975094 * q^77 + 16950730 * q^78 + 98292 * q^80 + 16674416 * q^81 - 780 * q^82 - 49131012 * q^83 - 4 * q^85 - 11166664 * q^86 + 4897380 * q^87 + 4260354 * q^88 - 36049824 * q^90 - 16 * q^91 + 506620 * q^92 + 22201162 * q^93 + 61024420 * q^95 + 32104128 * 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.