Properties

Label 2300.2.bt
Level $2300$
Weight $2$
Character orbit 2300.bt
Rep. character $\chi_{2300}(3,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $28480$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.bt (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2300 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

Total New Old
Modular forms 29120 29120 0
Cusp forms 28480 28480 0
Eisenstein series 640 640 0

Trace form

\( 28480 q - 72 q^{2} - 90 q^{4} - 144 q^{5} - 54 q^{6} - 72 q^{8} - 180 q^{9} + O(q^{10}) \) \( 28480 q - 72 q^{2} - 90 q^{4} - 144 q^{5} - 54 q^{6} - 72 q^{8} - 180 q^{9} - 72 q^{10} - 84 q^{12} - 144 q^{13} - 90 q^{14} - 54 q^{16} - 144 q^{17} - 52 q^{18} - 76 q^{20} - 108 q^{21} - 172 q^{22} - 144 q^{25} - 144 q^{26} - 56 q^{28} - 180 q^{29} - 92 q^{30} - 92 q^{32} - 120 q^{33} - 90 q^{34} - 22 q^{36} - 144 q^{37} - 80 q^{38} - 192 q^{40} - 108 q^{41} + 112 q^{42} - 90 q^{44} - 280 q^{45} - 60 q^{46} - 300 q^{48} - 236 q^{50} - 20 q^{52} - 96 q^{53} - 350 q^{54} - 54 q^{56} - 136 q^{57} - 32 q^{58} - 48 q^{60} - 108 q^{61} - 108 q^{62} - 90 q^{64} - 112 q^{65} - 6 q^{66} - 196 q^{68} - 200 q^{69} - 216 q^{70} - 256 q^{72} - 144 q^{73} - 176 q^{76} - 136 q^{77} - 100 q^{78} - 294 q^{80} - 756 q^{81} - 80 q^{82} + 70 q^{84} + 72 q^{85} - 54 q^{86} - 40 q^{88} - 180 q^{89} - 354 q^{90} + 22 q^{92} - 472 q^{93} - 90 q^{94} - 94 q^{96} - 144 q^{97} - 20 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) into newform subspaces

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