Properties

Label 2800.2.dg
Level $2800$
Weight $2$
Character orbit 2800.dg
Rep. character $\chi_{2800}(451,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1192$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.dg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

Total New Old
Modular forms 1968 1240 728
Cusp forms 1872 1192 680
Eisenstein series 96 48 48

Trace form

\( 1192 q + 2 q^{2} + 6 q^{3} + 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 1192 q + 2 q^{2} + 6 q^{3} + 8 q^{7} - 4 q^{8} - 2 q^{11} + 6 q^{12} + 4 q^{16} + 12 q^{17} - 10 q^{18} + 6 q^{19} - 6 q^{21} - 12 q^{22} - 4 q^{23} + 6 q^{24} - 18 q^{26} + 18 q^{28} - 8 q^{29} - 8 q^{32} + 12 q^{33} - 112 q^{36} + 10 q^{37} + 6 q^{38} + 4 q^{39} - 10 q^{42} + 16 q^{43} + 14 q^{44} - 4 q^{46} + 8 q^{49} - 14 q^{51} - 12 q^{52} + 10 q^{53} - 42 q^{54} + 64 q^{56} - 10 q^{58} - 42 q^{59} - 18 q^{61} + 96 q^{64} - 30 q^{66} + 34 q^{67} + 36 q^{68} + 16 q^{71} - 32 q^{72} + 34 q^{74} - 10 q^{77} - 52 q^{78} + 488 q^{81} - 42 q^{82} - 40 q^{84} + 52 q^{86} + 12 q^{87} - 10 q^{88} - 80 q^{91} - 108 q^{92} - 10 q^{93} - 30 q^{94} + 144 q^{96} - 52 q^{98} + 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)