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Properties

Label 1872.4.ed
Level $1872$
Weight $4$
Character orbit 1872.ed
Rep. character $\chi_{1872}(19,\cdot)$
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.ed (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

\( 1672 q + 4 q^{2} - 6 q^{4} - 8 q^{7} - 2 q^{8} + O(q^{10}) \) \( 1672 q + 4 q^{2} - 6 q^{4} - 8 q^{7} - 2 q^{8} + 82 q^{10} + 6 q^{11} - 4 q^{13} - 200 q^{14} - 170 q^{16} + 12 q^{17} - 6 q^{19} + 18 q^{20} + 214 q^{22} + 12 q^{23} - 41000 q^{25} - 100 q^{26} - 476 q^{28} + 2 q^{29} - 576 q^{32} - 342 q^{34} - 748 q^{35} - 2 q^{37} - 1388 q^{38} + 1552 q^{40} + 426 q^{43} + 56 q^{44} - 670 q^{46} - 12 q^{49} - 990 q^{50} - 838 q^{52} + 8 q^{53} - 292 q^{55} + 656 q^{56} + 3198 q^{58} + 2070 q^{59} - 2 q^{61} - 2928 q^{62} + 3192 q^{64} + 8 q^{65} - 6 q^{67} - 258 q^{68} + 824 q^{70} + 232 q^{71} - 296 q^{73} + 1686 q^{74} - 4260 q^{76} + 1372 q^{77} + 148 q^{80} - 6524 q^{82} + 248 q^{85} + 132 q^{86} + 5128 q^{88} + 88 q^{89} - 586 q^{91} + 960 q^{92} + 2040 q^{94} - 500 q^{95} - 8 q^{97} + 6592 q^{98} + O(q^{100}) \)

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

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