Properties

Label 1872.2.u
Level $1872$
Weight $2$
Character orbit 1872.u
Rep. character $\chi_{1872}(1243,\cdot)$
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.u (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

\( 276 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 276 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + 16 q^{10} - 2 q^{13} - 12 q^{14} - 4 q^{16} + 12 q^{20} - 12 q^{22} - 260 q^{25} - 18 q^{26} + 28 q^{28} + 4 q^{29} - 8 q^{32} - 8 q^{34} + 4 q^{35} - 4 q^{37} - 8 q^{38} + 36 q^{40} + 16 q^{43} - 8 q^{44} + 16 q^{46} + 14 q^{50} - 40 q^{52} + 4 q^{53} + 24 q^{55} + 20 q^{56} - 28 q^{58} - 4 q^{61} + 36 q^{64} + 4 q^{65} - 24 q^{68} + 32 q^{70} + 36 q^{71} - 8 q^{73} + 60 q^{74} + 8 q^{76} - 28 q^{77} - 60 q^{80} - 24 q^{82} + 16 q^{85} - 64 q^{86} + 32 q^{88} - 8 q^{89} + 20 q^{91} + 4 q^{94} - 40 q^{95} - 4 q^{97} + 30 q^{98} + O(q^{100}) \)

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

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