↑

Properties

Label 1872.4.u
Level $1872$
Weight $4$
Character orbit 1872.u
Rep. character $\chi_{1872}(1243,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $836$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 2032 844 1188
Cusp forms 2000 836 1164
Eisenstein series 32 8 24

Trace form

\( 836 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 836 q + 2 q^{2} - 4 q^{7} + 8 q^{8} - 40 q^{10} - 2 q^{13} + 212 q^{14} - 4 q^{16} - 276 q^{20} - 220 q^{22} - 20500 q^{25} + 106 q^{26} - 100 q^{28} + 4 q^{29} + 72 q^{32} - 792 q^{34} + 4 q^{35} - 4 q^{37} - 352 q^{38} - 1564 q^{40} - 432 q^{43} - 200 q^{44} + 664 q^{46} + 294 q^{50} + 832 q^{52} + 4 q^{53} + 280 q^{55} + 1300 q^{56} + 900 q^{58} - 4 q^{61} - 1212 q^{64} + 4 q^{65} + 264 q^{68} + 1432 q^{70} - 220 q^{71} + 296 q^{73} - 3636 q^{74} - 216 q^{76} - 1372 q^{77} + 1748 q^{80} - 1192 q^{82} + 496 q^{85} + 5136 q^{86} + 2048 q^{88} - 88 q^{89} - 1964 q^{91} + 96 q^{92} - 5100 q^{94} - 1000 q^{95} - 4 q^{97} - 802 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)