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Properties

Label 1872.4.gq
Level $1872$
Weight $4$
Character orbit 1872.gq
Rep. character $\chi_{1872}(685,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1672$
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.gq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
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 4064 1688 2376
Cusp forms 4000 1672 2328
Eisenstein series 64 16 48

Trace form

\( 1672 q + 2 q^{2} - 2 q^{4} + 8 q^{5} + 8 q^{8} + O(q^{10}) \) \( 1672 q + 2 q^{2} - 2 q^{4} + 8 q^{5} + 8 q^{8} - 2 q^{10} + 2 q^{11} - 4 q^{13} - 168 q^{14} - 2 q^{16} + 4 q^{17} - 2 q^{19} - 38 q^{20} + 34 q^{22} - 248 q^{26} - 32 q^{28} + 2 q^{29} - 16 q^{31} + 482 q^{32} - 476 q^{34} - 248 q^{35} - 2 q^{37} + 228 q^{38} - 748 q^{40} - 434 q^{43} - 1224 q^{44} + 1756 q^{46} + 16 q^{47} + 39784 q^{49} + 2828 q^{50} - 922 q^{52} + 8 q^{53} - 1184 q^{56} - 1190 q^{58} + 2730 q^{59} - 2 q^{61} + 30 q^{62} + 532 q^{64} + 496 q^{65} - 2 q^{67} - 1256 q^{68} - 5480 q^{70} - 78 q^{74} - 2866 q^{76} + 1380 q^{77} - 6336 q^{79} - 4638 q^{80} - 1672 q^{82} + 2688 q^{83} - 252 q^{85} + 4800 q^{86} + 1980 q^{88} + 2806 q^{91} - 4584 q^{92} + 2114 q^{94} + 6084 q^{95} - 4 q^{97} - 2030 q^{98} + O(q^{100}) \)

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

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