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Properties

Label 495.4.bj
Level $495$
Weight $4$
Character orbit 495.bj
Rep. character $\chi_{495}(28,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $704$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(495, [\chi])\).

Total New Old
Modular forms 1792 736 1056
Cusp forms 1664 704 960
Eisenstein series 128 32 96

Trace form

\( 704 q + 10 q^{2} - 10 q^{5} + 10 q^{7} + 10 q^{8} + O(q^{10}) \) \( 704 q + 10 q^{2} - 10 q^{5} + 10 q^{7} + 10 q^{8} + 36 q^{11} - 10 q^{13} + 2556 q^{16} + 330 q^{17} - 436 q^{20} - 58 q^{22} - 336 q^{23} + 578 q^{25} + 436 q^{26} + 710 q^{28} - 444 q^{31} + 10 q^{35} - 174 q^{37} + 1082 q^{38} - 650 q^{40} - 2200 q^{41} - 3740 q^{46} + 370 q^{47} + 1370 q^{50} - 8530 q^{52} + 42 q^{53} - 1550 q^{55} + 4712 q^{56} + 1758 q^{58} - 500 q^{61} + 7880 q^{62} + 256 q^{67} - 5190 q^{68} - 650 q^{70} - 972 q^{71} - 7390 q^{73} - 4162 q^{77} - 2558 q^{80} - 4250 q^{82} - 6690 q^{83} - 170 q^{85} + 2756 q^{86} - 5890 q^{88} - 4616 q^{91} - 14680 q^{92} - 1370 q^{95} + 3510 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)