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Properties

Label 2975.2.fh
Level $2975$
Weight $2$
Character orbit 2975.fh
Rep. character $\chi_{2975}(23,\cdot)$
Character field $\Q(\zeta_{240})$
Dimension $22784$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2975 = 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2975.fh (of order \(240\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2975 \)
Character field: \(\Q(\zeta_{240})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2975, [\chi])\).

Total New Old
Modular forms 23296 23296 0
Cusp forms 22784 22784 0
Eisenstein series 512 512 0

Trace form

\( 22784 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 96 q^{6} - 64 q^{7} - 160 q^{8} - 40 q^{9} + O(q^{10}) \) \( 22784 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 96 q^{6} - 64 q^{7} - 160 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} + 16 q^{12} - 96 q^{13} - 80 q^{14} - 80 q^{15} - 32 q^{17} - 64 q^{18} - 40 q^{19} - 128 q^{20} - 48 q^{21} - 128 q^{22} - 32 q^{23} - 40 q^{25} - 64 q^{26} - 224 q^{27} - 160 q^{29} + 224 q^{30} - 24 q^{31} - 32 q^{32} - 160 q^{34} - 128 q^{35} - 96 q^{36} - 40 q^{38} + 8 q^{39} - 32 q^{40} - 96 q^{41} - 176 q^{42} - 128 q^{43} - 40 q^{44} - 32 q^{45} - 184 q^{46} - 40 q^{47} - 144 q^{48} + 64 q^{50} - 64 q^{51} - 64 q^{52} - 96 q^{53} - 40 q^{54} - 64 q^{55} - 48 q^{56} - 128 q^{57} - 32 q^{58} - 40 q^{59} + 96 q^{60} - 24 q^{61} - 512 q^{62} + 56 q^{63} - 160 q^{64} + 8 q^{65} - 24 q^{66} - 184 q^{68} - 320 q^{69} - 192 q^{70} - 96 q^{71} - 216 q^{72} + 8 q^{73} - 480 q^{75} - 256 q^{76} + 16 q^{77} - 64 q^{78} - 40 q^{79} - 48 q^{80} - 24 q^{81} - 32 q^{82} - 384 q^{83} + 32 q^{85} - 48 q^{86} + 16 q^{87} + 256 q^{88} - 40 q^{89} - 176 q^{90} + 512 q^{91} - 224 q^{92} + 296 q^{93} + 24 q^{94} - 128 q^{95} - 120 q^{96} - 320 q^{97} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2975, [\chi])\) into newform subspaces

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