↑

Properties

Label 1089.4.j
Level $1089$
Weight $4$
Character orbit 1089.j
Rep. character $\chi_{1089}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
Sturm bound $528$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1089, [\chi])\).

Total New Old
Modular forms 1680 432 1248
Cusp forms 1488 432 1056
Eisenstein series 192 0 192

Trace form

\( 432 q - 432 q^{4} + O(q^{10}) \) \( 432 q - 432 q^{4} - 1392 q^{16} + 1692 q^{25} + 1140 q^{28} + 1620 q^{31} + 1272 q^{34} + 240 q^{37} - 1440 q^{40} + 720 q^{46} + 7236 q^{49} - 8520 q^{52} - 5232 q^{58} + 1320 q^{61} + 4704 q^{64} + 7632 q^{67} + 2688 q^{70} + 7740 q^{73} - 5280 q^{79} - 6612 q^{82} - 11400 q^{85} - 3288 q^{91} - 2280 q^{94} + 6024 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)