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Properties

Label 630.4.u
Level $630$
Weight $4$
Character orbit 630.u
Rep. character $\chi_{630}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 896 120 776
Cusp forms 832 120 712
Eisenstein series 64 0 64

Trace form

\( 120 q + 240 q^{4} - 8 q^{5} + O(q^{10}) \) \( 120 q + 240 q^{4} - 8 q^{5} - 12 q^{10} - 78 q^{11} + 92 q^{14} - 960 q^{16} - 102 q^{19} - 64 q^{20} - 30 q^{25} + 388 q^{26} + 100 q^{29} + 476 q^{31} - 544 q^{34} - 296 q^{35} + 48 q^{40} - 1008 q^{41} + 312 q^{44} - 488 q^{46} - 1062 q^{49} + 1376 q^{50} - 1444 q^{55} + 208 q^{56} - 80 q^{59} - 2426 q^{61} - 7680 q^{64} + 62 q^{65} + 404 q^{70} - 4128 q^{71} - 1012 q^{74} - 816 q^{76} - 2276 q^{79} - 128 q^{80} - 4172 q^{85} - 556 q^{86} - 3830 q^{89} - 644 q^{91} + 2788 q^{94} + 3122 q^{95} + O(q^{100}) \)

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

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