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Properties

Label 1872.4.bm
Level $1872$
Weight $4$
Character orbit 1872.bm
Rep. character $\chi_{1872}(181,\cdot)$
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.bm (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

\( 836 q - 4 q^{4} + O(q^{10}) \) \( 836 q - 4 q^{4} - 4 q^{10} - 2 q^{13} + 244 q^{14} - 4 q^{16} + 8 q^{17} - 292 q^{22} + 264 q^{26} + 4 q^{29} + 504 q^{35} - 216 q^{38} + 2376 q^{40} - 436 q^{43} + 39780 q^{49} - 1172 q^{52} + 4 q^{53} + 876 q^{56} - 4 q^{61} + 1664 q^{62} - 544 q^{64} + 492 q^{65} - 4312 q^{68} + 1744 q^{74} + 1376 q^{77} + 3152 q^{79} + 4320 q^{82} + 5688 q^{88} - 1640 q^{91} + 2868 q^{92} + 4292 q^{94} - 6072 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \)