↑

Properties

Label 1815.4.k
Level $1815$
Weight $4$
Character orbit 1815.k
Rep. character $\chi_{1815}(122,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1272$
Sturm bound $1056$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1815, [\chi])\).

Total New Old
Modular forms 1632 1344 288
Cusp forms 1536 1272 264
Eisenstein series 96 72 24

Trace form

\( 1272 q + 6 q^{3} - 4 q^{6} + 16 q^{7} + O(q^{10}) \) \( 1272 q + 6 q^{3} - 4 q^{6} + 16 q^{7} + 100 q^{10} - 152 q^{12} - 20 q^{13} + 78 q^{15} - 18388 q^{16} - 204 q^{18} - 260 q^{21} + 220 q^{25} + 114 q^{27} + 356 q^{28} + 164 q^{30} + 200 q^{31} + 132 q^{36} - 428 q^{37} + 192 q^{40} - 272 q^{42} - 548 q^{43} + 1592 q^{45} + 464 q^{46} - 3532 q^{48} + 884 q^{51} - 680 q^{52} + 356 q^{57} - 252 q^{58} + 1068 q^{60} + 224 q^{61} + 1220 q^{63} - 444 q^{67} - 6444 q^{70} + 1344 q^{72} - 1088 q^{73} - 2378 q^{75} - 1200 q^{76} - 4900 q^{78} - 3192 q^{81} - 1144 q^{82} + 2788 q^{85} - 352 q^{87} - 7544 q^{90} - 3592 q^{91} - 496 q^{93} + 1012 q^{96} + 1360 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)