↑

Properties

Label 675.4.w
Level $675$
Weight $4$
Character orbit 675.w
Rep. character $\chi_{675}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(675, [\chi])\).

Total New Old
Modular forms 2208 960 1248
Cusp forms 2112 960 1152
Eisenstein series 96 0 96

Trace form

\( 960 q + 12 q^{7} + O(q^{10}) \) \( 960 q + 12 q^{7} + 96 q^{10} + 3840 q^{16} + 120 q^{19} - 192 q^{22} - 72 q^{25} - 1008 q^{28} - 5280 q^{34} - 1368 q^{37} + 2580 q^{40} + 1464 q^{43} - 804 q^{52} - 756 q^{55} - 5928 q^{58} - 2880 q^{64} + 1536 q^{67} - 3900 q^{70} + 3300 q^{73} + 2160 q^{79} + 7956 q^{82} - 21720 q^{85} + 5568 q^{88} + 22080 q^{94} - 11040 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)