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Properties

Label 1872.4.gy
Level $1872$
Weight $4$
Character orbit 1872.gy
Rep. character $\chi_{1872}(277,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.gy (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1872 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 4048 4048 0
Cusp forms 4016 4016 0
Eisenstein series 32 32 0

Trace form

\( 4016 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} + O(q^{10}) \) \( 4016 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 4 q^{10} - 6 q^{11} + 148 q^{12} - 2 q^{13} - 36 q^{14} - 12 q^{15} + 2 q^{16} - 8 q^{17} + 48 q^{18} - 12 q^{19} - 162 q^{21} + 2 q^{22} + 1098 q^{24} - 280 q^{26} - 140 q^{27} - 12 q^{28} + 2 q^{29} - 34 q^{30} - 6 q^{32} - 12 q^{33} - 48 q^{34} + 246 q^{35} + 762 q^{36} - 12 q^{37} - 4 q^{38} - 4 q^{40} - 1050 q^{42} - 4 q^{43} - 6 q^{45} - 12 q^{46} - 1184 q^{48} + 192072 q^{49} + 100 q^{51} - 2 q^{52} - 16 q^{53} - 6 q^{54} + 624 q^{56} - 6 q^{58} - 6 q^{59} + 384 q^{60} - 4 q^{61} + 958 q^{62} - 12 q^{63} - 556 q^{64} - 4 q^{65} + 5500 q^{66} + 3576 q^{68} + 214 q^{69} - 2058 q^{70} - 3078 q^{72} - 3644 q^{74} + 140 q^{75} - 1376 q^{77} - 2402 q^{78} - 8 q^{79} - 12 q^{80} - 4 q^{81} + 666 q^{82} - 2064 q^{84} + 744 q^{85} - 2086 q^{88} - 9372 q^{90} - 694 q^{91} + 252 q^{92} - 168 q^{93} - 68 q^{94} - 12156 q^{95} - 9264 q^{96} - 2070 q^{98} + 4374 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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