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

• Label: 630.4.j
• Level: $630$
• Weight: $4$
• Character orbit: 630.j
• Rep. character: $\chi_{630}(211,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $144$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	880	144	736
Cusp forms	848	144	704
Eisenstein series	32	0	32

Trace form

144 * q + 8 * q^2 - 4 * q^3 - 288 * q^4 - 40 * q^6 - 64 * q^8 - 44 * q^9 + 92 * q^11 + 32 * q^12 - 40 * q^15 - 1152 * q^16 - 152 * q^17 + 368 * q^18 + 360 * q^19 - 112 * q^21 - 72 * q^22 - 160 * q^24 - 1800 * q^25 - 664 * q^27 - 896 * q^29 + 128 * q^32 - 308 * q^33 + 360 * q^34 - 280 * q^35 + 208 * q^36 + 424 * q^38 - 144 * q^39 - 532 * q^41 + 684 * q^43 - 736 * q^44 + 320 * q^45 - 1632 * q^47 - 64 * q^48 - 3528 * q^49 + 200 * q^50 - 744 * q^51 - 1136 * q^53 + 1352 * q^54 - 3588 * q^57 - 796 * q^59 - 160 * q^60 + 1248 * q^62 + 224 * q^63 + 9216 * q^64 + 1680 * q^65 + 240 * q^66 + 1548 * q^67 + 304 * q^68 + 232 * q^69 + 56 * q^71 - 736 * q^72 + 1656 * q^73 - 608 * q^74 - 100 * q^75 - 720 * q^76 + 1232 * q^77 - 2896 * q^78 - 936 * q^79 - 5468 * q^81 - 4176 * q^82 - 888 * q^83 + 896 * q^84 - 720 * q^85 - 568 * q^86 + 5424 * q^87 - 288 * q^88 + 7520 * q^89 + 320 * q^90 + 1008 * q^91 - 1136 * q^93 + 2080 * q^95 + 1280 * q^96 + 36 * q^97 - 784 * q^98 + 12580 * 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

\( S_{4}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)