Space of modular forms of level 315, weight 10, and Character 315.bx

• Label: 315.10.bx
• Level: $315$
• Weight: $10$
• Character orbit: 315.bx
• Rep. character: $\chi_{315}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1712$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.bx (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	1744	1744	0
Cusp forms	1712	1712	0
Eisenstein series	32	32	0

Trace form

1712 * q - 6 * q^2 - 2 * q^3 + 9072 * q^6 - 2 * q^7 - 4 * q^10 - 80782 * q^12 - 4 * q^13 - 120884 * q^15 + 54525956 * q^16 + 1578672 * q^17 + 554750 * q^18 - 12 * q^20 - 3484396 * q^21 + 2044 * q^22 - 4 * q^25 - 6937052 * q^27 + 523256 * q^28 - 28408880 * q^30 + 4 * q^31 + 47214270 * q^32 + 8584022 * q^33 + 51222512 * q^36 - 4 * q^37 - 2097156 * q^40 + 6695388 * q^41 - 16347646 * q^42 - 4 * q^43 + 79335022 * q^45 + 12858040 * q^46 - 6 * q^47 + 81105458 * q^48 - 230399244 * q^50 - 6528388 * q^51 - 2101252 * q^52 + 7812484 * q^55 + 204952512 * q^56 - 93078508 * q^57 + 205950588 * q^58 - 45210374 * q^60 - 24455624 * q^61 - 325058506 * q^63 + 1326905202 * q^65 + 1564182892 * q^66 + 2 * q^67 - 15625002 * q^70 - 57106126 * q^72 - 4 * q^73 + 133741974 * q^75 - 1048584 * q^76 + 2037024042 * q^77 + 271275054 * q^78 + 21864636 * q^80 + 586546232 * q^81 - 1028 * q^82 - 12 * q^83 - 4 * q^85 + 830173232 * q^87 + 534777852 * q^88 + 970387476 * q^90 - 16 * q^91 + 6478500852 * q^92 + 1830534394 * q^93 - 23437506 * q^95 - 10481173236 * q^96 - 4 * q^97 + 3072 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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