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

• Label: 630.4.z
• Level: $630$
• Weight: $4$
• Character orbit: 630.z
• Rep. character: $\chi_{630}(169,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	880	216	664
Cusp forms	848	216	632
Eisenstein series	32	0	32

Trace form

216 * q + 432 * q^4 + 16 * q^5 + 64 * q^9 + 96 * q^11 - 112 * q^14 + 188 * q^15 - 1728 * q^16 - 64 * q^20 + 112 * q^21 + 288 * q^25 - 1112 * q^29 + 176 * q^30 - 144 * q^31 + 896 * q^36 + 584 * q^39 + 512 * q^41 + 768 * q^44 + 1884 * q^45 + 5292 * q^49 + 376 * q^50 + 3884 * q^51 - 1296 * q^54 + 1584 * q^55 + 448 * q^56 - 2584 * q^59 + 352 * q^60 - 13824 * q^64 + 1704 * q^65 - 1040 * q^66 + 5480 * q^69 - 4376 * q^71 - 3568 * q^74 + 2208 * q^75 - 936 * q^79 - 512 * q^80 - 688 * q^81 + 896 * q^84 - 1656 * q^85 + 2048 * q^86 - 1280 * q^89 - 2520 * q^90 - 1008 * q^91 - 2028 * q^95 - 4188 * q^99

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

\( S_{4}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)