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Properties

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 $576$

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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

\( 144 q + 8 q^{2} - 4 q^{3} - 288 q^{4} - 40 q^{6} - 64 q^{8} - 44 q^{9} + O(q^{10}) \) \( 144 q + 8 q^{2} - 4 q^{3} - 288 q^{4} - 40 q^{6} - 64 q^{8} - 44 q^{9} + 92 q^{11} + 32 q^{12} - 40 q^{15} - 1152 q^{16} - 152 q^{17} + 368 q^{18} + 360 q^{19} - 112 q^{21} - 72 q^{22} - 160 q^{24} - 1800 q^{25} - 664 q^{27} - 896 q^{29} + 128 q^{32} - 308 q^{33} + 360 q^{34} - 280 q^{35} + 208 q^{36} + 424 q^{38} - 144 q^{39} - 532 q^{41} + 684 q^{43} - 736 q^{44} + 320 q^{45} - 1632 q^{47} - 64 q^{48} - 3528 q^{49} + 200 q^{50} - 744 q^{51} - 1136 q^{53} + 1352 q^{54} - 3588 q^{57} - 796 q^{59} - 160 q^{60} + 1248 q^{62} + 224 q^{63} + 9216 q^{64} + 1680 q^{65} + 240 q^{66} + 1548 q^{67} + 304 q^{68} + 232 q^{69} + 56 q^{71} - 736 q^{72} + 1656 q^{73} - 608 q^{74} - 100 q^{75} - 720 q^{76} + 1232 q^{77} - 2896 q^{78} - 936 q^{79} - 5468 q^{81} - 4176 q^{82} - 888 q^{83} + 896 q^{84} - 720 q^{85} - 568 q^{86} + 5424 q^{87} - 288 q^{88} + 7520 q^{89} + 320 q^{90} + 1008 q^{91} - 1136 q^{93} + 2080 q^{95} + 1280 q^{96} + 36 q^{97} - 784 q^{98} + 12580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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