↑

Properties

Label 495.4.k
Level $495$
Weight $4$
Character orbit 495.k
Rep. character $\chi_{495}(208,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
Sturm bound $288$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 448 184 264
Cusp forms 416 176 240
Eisenstein series 32 8 24

Trace form

\( 176 q + 20 q^{5} + O(q^{10}) \) \( 176 q + 20 q^{5} - 16 q^{11} - 2576 q^{16} - 504 q^{20} + 48 q^{22} - 224 q^{23} - 228 q^{25} - 416 q^{26} + 424 q^{31} + 164 q^{37} - 952 q^{38} - 420 q^{47} + 1528 q^{53} - 620 q^{55} + 4008 q^{56} - 88 q^{58} + 1704 q^{67} + 2320 q^{70} + 992 q^{71} - 1188 q^{77} - 3832 q^{80} - 4040 q^{82} - 9696 q^{86} - 1080 q^{88} - 2584 q^{91} + 4200 q^{92} - 6340 q^{97} + O(q^{100}) \)

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

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