Space of modular forms of level 315, weight 4, and Character 315.bx

• Label: 315.4.bx
• Level: $315$
• Weight: $4$
• Character orbit: 315.bx
• Rep. character: $\chi_{315}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $560$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.bx (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	592	592	0
Cusp forms	560	560	0
Eisenstein series	32	32	0

Trace form

560 * q - 6 * q^2 - 2 * q^3 - 2 * q^7 - 4 * q^10 - 142 * q^12 - 4 * q^13 + 76 * q^15 + 4100 * q^16 + 144 * q^17 + 62 * q^18 - 12 * q^20 - 244 * q^21 + 28 * q^22 - 4 * q^25 + 4 * q^27 + 104 * q^28 + 1240 * q^30 + 4 * q^31 + 990 * q^32 - 106 * q^33 + 1424 * q^36 - 4 * q^37 - 516 * q^40 - 1260 * q^41 - 406 * q^42 - 4 * q^43 + 382 * q^45 - 512 * q^46 - 6 * q^47 + 1778 * q^48 - 684 * q^50 + 1148 * q^51 - 580 * q^52 + 484 * q^55 + 3936 * q^56 + 68 * q^57 + 1068 * q^58 - 854 * q^60 - 32 * q^61 - 4714 * q^63 + 2082 * q^65 + 2764 * q^66 + 2 * q^67 - 1002 * q^70 + 818 * q^72 - 4 * q^73 + 534 * q^75 - 264 * q^76 + 3210 * q^77 + 654 * q^78 + 1116 * q^80 - 2992 * q^81 - 20 * q^82 - 12 * q^83 - 4 * q^85 + 3584 * q^87 + 1596 * q^88 - 1524 * q^90 - 16 * q^91 + 3780 * q^92 - 1382 * q^93 - 1506 * q^95 - 5364 * q^96 - 4 * q^97 + 48 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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