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Properties

Label 490.6.l
Level $490$
Weight $6$
Character orbit 490.l
Rep. character $\chi_{490}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $400$
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.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1744 400 1344
Cusp forms 1616 400 1216
Eisenstein series 128 0 128

Trace form

\( 400 q + 132 q^{5} + O(q^{10}) \) \( 400 q + 132 q^{5} - 1488 q^{10} - 1500 q^{11} - 5136 q^{15} + 51200 q^{16} - 3204 q^{17} - 4544 q^{18} + 4704 q^{22} - 19196 q^{23} + 660 q^{25} + 2640 q^{26} + 20112 q^{30} - 4920 q^{31} - 73608 q^{33} - 558720 q^{36} - 31636 q^{37} + 2976 q^{38} + 158072 q^{43} - 6108 q^{45} + 7040 q^{46} - 83292 q^{47} - 51328 q^{50} + 155280 q^{51} - 54060 q^{53} + 288072 q^{57} + 51872 q^{58} - 15616 q^{60} + 205260 q^{61} + 79896 q^{65} - 147568 q^{67} - 51264 q^{68} - 252880 q^{71} - 72704 q^{72} - 491628 q^{73} + 575088 q^{75} + 408320 q^{78} + 33792 q^{80} + 1323120 q^{81} - 236352 q^{82} - 1018888 q^{85} - 34800 q^{86} - 517896 q^{87} + 37632 q^{88} + 614272 q^{92} - 137612 q^{93} - 35932 q^{95} + 61440 q^{96} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)