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Properties

Label 490.4.i
Level $490$
Weight $4$
Character orbit 490.i
Rep. character $\chi_{490}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(490, [\chi])\).

Total New Old
Modular forms 536 120 416
Cusp forms 472 120 352
Eisenstein series 64 0 64

Trace form

\( 120 q + 240 q^{4} + 8 q^{5} - 56 q^{6} + 618 q^{9} + O(q^{10}) \) \( 120 q + 240 q^{4} + 8 q^{5} - 56 q^{6} + 618 q^{9} - 12 q^{10} + 54 q^{11} - 260 q^{15} - 960 q^{16} - 186 q^{19} + 64 q^{20} - 112 q^{24} - 98 q^{25} + 236 q^{26} + 1156 q^{29} - 140 q^{30} + 652 q^{31} + 544 q^{34} + 4944 q^{36} + 1120 q^{39} + 48 q^{40} - 792 q^{41} - 216 q^{44} - 664 q^{45} - 808 q^{46} + 2272 q^{50} + 1972 q^{51} - 1540 q^{54} - 596 q^{55} - 1336 q^{59} - 520 q^{60} + 314 q^{61} - 7680 q^{64} - 2926 q^{65} + 1600 q^{66} - 180 q^{69} - 5952 q^{71} + 204 q^{74} + 4550 q^{75} - 1488 q^{76} + 4048 q^{79} + 128 q^{80} - 7244 q^{81} - 8876 q^{85} - 484 q^{86} - 6094 q^{89} - 200 q^{90} - 3604 q^{94} - 1590 q^{95} + 448 q^{96} + 24748 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)