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Properties

Label 1872.4.bq
Level $1872$
Weight $4$
Character orbit 1872.bq
Rep. character $\chi_{1872}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $836$
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.bq (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2032 844 1188
Cusp forms 2000 836 1164
Eisenstein series 32 8 24

Trace form

\( 836 q + 2 q^{2} + 4 q^{5} - 4 q^{7} - 4 q^{8} + O(q^{10}) \) \( 836 q + 2 q^{2} + 4 q^{5} - 4 q^{7} - 4 q^{8} + 40 q^{10} + 4 q^{11} - 2 q^{13} + 212 q^{14} - 4 q^{16} - 4 q^{19} + 360 q^{20} - 220 q^{22} + 20500 q^{25} + 442 q^{26} - 100 q^{28} + 4 q^{29} + 212 q^{32} + 320 q^{34} + 4 q^{35} + 352 q^{38} - 1564 q^{40} + 432 q^{43} - 1028 q^{44} + 1504 q^{46} - 970 q^{50} + 712 q^{52} + 4 q^{53} + 280 q^{55} - 1300 q^{56} - 2092 q^{58} + 668 q^{59} - 4 q^{61} + 1212 q^{64} + 4 q^{65} - 4 q^{67} + 264 q^{68} - 1140 q^{70} - 220 q^{71} - 296 q^{73} - 3636 q^{74} - 492 q^{76} + 1372 q^{77} - 6384 q^{80} + 1192 q^{82} + 2684 q^{83} - 440 q^{86} - 2048 q^{88} + 88 q^{89} - 3336 q^{91} + 96 q^{92} - 5100 q^{94} + 1000 q^{95} - 4 q^{97} - 482 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)