↑

Properties

Label 1848.2.g
Level $1848$
Weight $2$
Character orbit 1848.g
Rep. character $\chi_{1848}(925,\cdot)$
Character field $\Q$
Dimension $120$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 392 120 272
Cusp forms 376 120 256
Eisenstein series 16 0 16

Trace form

\( 120 q - 8 q^{4} - 8 q^{6} - 120 q^{9} + O(q^{10}) \) \( 120 q - 8 q^{4} - 8 q^{6} - 120 q^{9} + 8 q^{10} + 16 q^{15} + 8 q^{16} - 16 q^{17} + 8 q^{24} - 104 q^{25} - 32 q^{31} + 8 q^{36} - 8 q^{40} + 16 q^{41} + 120 q^{49} + 8 q^{54} - 12 q^{58} + 4 q^{60} + 48 q^{62} - 68 q^{64} + 64 q^{65} + 48 q^{68} + 12 q^{70} - 80 q^{73} - 112 q^{74} + 64 q^{76} + 12 q^{78} + 32 q^{79} - 24 q^{80} + 120 q^{81} - 8 q^{82} + 24 q^{86} - 12 q^{88} - 80 q^{89} - 8 q^{90} + 8 q^{92} + 104 q^{94} - 48 q^{96} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \)