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Properties

Label 1476.2.ch
Level $1476$
Weight $2$
Character orbit 1476.ch
Rep. character $\chi_{1476}(131,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3968$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.ch (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1476 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

Total New Old
Modular forms 4096 4096 0
Cusp forms 3968 3968 0
Eisenstein series 128 128 0

Trace form

\( 3968 q - 30 q^{2} - 6 q^{4} - 60 q^{5} - 6 q^{6} + O(q^{10}) \) \( 3968 q - 30 q^{2} - 6 q^{4} - 60 q^{5} - 6 q^{6} - 40 q^{10} - 22 q^{12} - 16 q^{13} - 24 q^{14} - 6 q^{16} - 30 q^{20} - 40 q^{21} - 28 q^{24} + 452 q^{25} - 16 q^{28} - 144 q^{29} - 54 q^{30} - 40 q^{33} - 4 q^{34} - 60 q^{36} - 48 q^{37} + 48 q^{38} + 4 q^{40} - 48 q^{41} + 40 q^{42} + 36 q^{45} - 40 q^{46} + 58 q^{48} - 20 q^{49} - 6 q^{52} - 68 q^{54} - 402 q^{56} + 16 q^{57} + 2 q^{58} - 20 q^{61} - 132 q^{64} - 48 q^{65} + 40 q^{66} - 48 q^{68} - 52 q^{69} - 46 q^{70} - 164 q^{72} - 30 q^{74} - 16 q^{76} - 60 q^{77} - 72 q^{78} - 24 q^{81} - 40 q^{82} - 20 q^{84} + 4 q^{85} - 18 q^{86} + 160 q^{90} - 18 q^{92} + 28 q^{93} - 48 q^{94} - 24 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

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