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Properties

Label 630.4.t
Level $630$
Weight $4$
Character orbit 630.t
Rep. character $\chi_{630}(311,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 880 192 688
Cusp forms 848 192 656
Eisenstein series 32 0 32

Trace form

\( 192 q + 384 q^{4} + 24 q^{7} - 18 q^{9} + O(q^{10}) \) \( 192 q + 384 q^{4} + 24 q^{7} - 18 q^{9} + 144 q^{13} + 132 q^{14} + 40 q^{15} - 1536 q^{16} + 112 q^{18} - 434 q^{21} - 48 q^{24} + 4800 q^{25} + 240 q^{26} - 72 q^{27} - 96 q^{28} - 42 q^{29} + 280 q^{30} + 180 q^{31} + 744 q^{33} + 240 q^{36} + 336 q^{37} - 276 q^{39} - 618 q^{41} + 160 q^{42} + 84 q^{43} + 96 q^{44} + 330 q^{45} + 252 q^{46} - 396 q^{47} + 876 q^{49} - 748 q^{51} - 72 q^{53} - 360 q^{54} - 96 q^{57} + 3000 q^{59} + 320 q^{60} - 4986 q^{61} + 748 q^{63} - 12288 q^{64} - 1920 q^{65} + 2400 q^{66} + 1176 q^{67} - 180 q^{70} - 448 q^{72} - 6312 q^{77} - 2144 q^{78} - 1776 q^{79} + 3826 q^{81} - 2584 q^{84} - 720 q^{85} - 516 q^{87} - 318 q^{89} + 180 q^{91} + 2016 q^{92} - 6736 q^{93} - 192 q^{96} + 3168 q^{97} - 2208 q^{98} + 6660 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)