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Properties

Label 490.6.g
Level $490$
Weight $6$
Character orbit 490.g
Rep. character $\chi_{490}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 490.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(490, [\chi])\).

Total New Old
Modular forms 872 200 672
Cusp forms 808 200 608
Eisenstein series 64 0 64

Trace form

\( 200 q + O(q^{10}) \) \( 200 q + 1560 q^{11} + 5136 q^{15} - 51200 q^{16} + 4544 q^{18} + 6624 q^{22} + 15368 q^{23} - 13992 q^{25} - 9888 q^{30} - 261120 q^{36} + 15400 q^{37} - 60200 q^{43} + 14080 q^{46} + 51328 q^{50} - 92640 q^{51} - 156480 q^{53} - 133512 q^{57} - 11744 q^{58} + 15616 q^{60} - 299136 q^{65} - 30080 q^{67} - 183920 q^{71} + 72704 q^{72} + 154048 q^{78} - 978840 q^{81} + 376 q^{85} - 310560 q^{86} - 105984 q^{88} + 245888 q^{92} + 1336760 q^{93} + 1193368 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)