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Properties

Label 495.4.ba
Level $495$
Weight $4$
Character orbit 495.ba
Rep. character $\chi_{495}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $352$
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.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(288\)

Dimensions

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

Total New Old
Modular forms 896 368 528
Cusp forms 832 352 480
Eisenstein series 64 16 48

Trace form

\( 352 q + 338 q^{4} - q^{5} + O(q^{10}) \) \( 352 q + 338 q^{4} - q^{5} + 24 q^{10} - 30 q^{11} + 102 q^{14} - 1594 q^{16} - 274 q^{19} + 200 q^{20} - 467 q^{25} + 524 q^{26} + 562 q^{29} - 582 q^{31} + 560 q^{34} + 959 q^{35} - 2358 q^{40} + 208 q^{41} - 3826 q^{44} + 3214 q^{46} + 2020 q^{49} + 1340 q^{50} + 1361 q^{55} + 2264 q^{56} + 910 q^{59} + 990 q^{61} + 9782 q^{64} - 1142 q^{65} + 3550 q^{70} - 2166 q^{71} - 3396 q^{74} - 6620 q^{76} - 1382 q^{79} - 904 q^{80} + 1143 q^{85} + 5918 q^{86} - 3084 q^{89} - 12 q^{91} - 7312 q^{94} + 321 q^{95} + O(q^{100}) \)

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

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