Space of modular forms of level 630, weight 4, and Character 630.bv

• Label: 630.4.bv
• Level: $630$
• Weight: $4$
• Character orbit: 630.bv
• Rep. character: $\chi_{630}(73,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $240$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).

	Total	New	Old
Modular forms	1792	240	1552
Cusp forms	1664	240	1424
Eisenstein series	128	0	128

Trace form

240 * q + 48 * q^5 + 20 * q^7 + 72 * q^10 + 12 * q^11 + 1920 * q^16 - 288 * q^17 - 624 * q^22 - 44 * q^23 + 296 * q^25 + 456 * q^26 + 16 * q^28 - 528 * q^31 - 1688 * q^35 - 120 * q^37 - 528 * q^38 + 832 * q^43 + 896 * q^46 + 1464 * q^47 - 448 * q^50 + 1696 * q^53 - 416 * q^56 + 688 * q^58 + 5292 * q^61 - 4 * q^65 + 80 * q^67 - 1152 * q^68 + 2424 * q^70 + 1664 * q^71 + 2160 * q^73 - 412 * q^77 + 768 * q^80 - 864 * q^82 + 1816 * q^85 - 1128 * q^86 - 1248 * q^88 - 3936 * q^91 + 352 * q^92 - 1664 * q^95 + 5552 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)