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Properties

Label 1872.2.bm
Level $1872$
Weight $2$
Character orbit 1872.bm
Rep. character $\chi_{1872}(181,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $276$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 688 284 404
Cusp forms 656 276 380
Eisenstein series 32 8 24

Trace form

\( 276 q - 4 q^{4} + O(q^{10}) \) \( 276 q - 4 q^{4} - 4 q^{10} - 2 q^{13} - 4 q^{14} - 4 q^{16} + 8 q^{17} + 28 q^{22} - 4 q^{26} + 4 q^{29} + 24 q^{35} - 16 q^{38} - 24 q^{40} + 12 q^{43} + 244 q^{49} - 12 q^{52} + 4 q^{53} + 12 q^{56} - 4 q^{61} - 16 q^{62} + 32 q^{64} - 4 q^{65} + 40 q^{68} - 72 q^{74} + 32 q^{77} - 48 q^{79} - 48 q^{82} - 40 q^{88} + 24 q^{91} + 36 q^{92} + 60 q^{94} + 72 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \)