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Properties

Label 490.4.l
Level $490$
Weight $4$
Character orbit 490.l
Rep. character $\chi_{490}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
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.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1072 240 832
Cusp forms 944 240 704
Eisenstein series 128 0 128

Trace form

\( 240 q - 48 q^{5} + O(q^{10}) \) \( 240 q - 48 q^{5} + 72 q^{10} - 60 q^{11} + 504 q^{15} + 1920 q^{16} - 288 q^{17} - 32 q^{18} - 912 q^{22} + 532 q^{23} - 80 q^{25} - 456 q^{26} + 72 q^{30} + 528 q^{31} + 1956 q^{33} - 7392 q^{36} + 768 q^{37} + 528 q^{38} - 2784 q^{43} - 4128 q^{45} - 896 q^{46} - 1464 q^{47} - 448 q^{50} + 1008 q^{51} + 360 q^{53} - 2016 q^{57} - 144 q^{58} + 704 q^{60} + 5076 q^{61} - 324 q^{65} + 2864 q^{67} - 1152 q^{68} + 2912 q^{71} - 128 q^{72} + 5616 q^{73} - 5232 q^{75} + 7040 q^{78} - 768 q^{80} + 1872 q^{81} - 864 q^{82} - 2088 q^{85} - 600 q^{86} - 15732 q^{87} - 1824 q^{88} - 4256 q^{92} + 2344 q^{93} + 3608 q^{95} + 384 q^{96} + O(q^{100}) \)

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

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