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Properties

Label 1872.2.ey
Level $1872$
Weight $2$
Character orbit 1872.ey
Rep. character $\chi_{1872}(829,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $552$
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.ey (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 568 808
Cusp forms 1312 552 760
Eisenstein series 64 16 48

Trace form

\( 552 q + 6 q^{2} - 2 q^{4} + O(q^{10}) \) \( 552 q + 6 q^{2} - 2 q^{4} - 2 q^{10} + 6 q^{11} - 4 q^{13} + 16 q^{14} - 2 q^{16} + 4 q^{17} - 6 q^{19} - 18 q^{20} + 2 q^{22} + 40 q^{26} + 2 q^{29} + 66 q^{32} + 12 q^{35} - 6 q^{37} + 28 q^{38} + 12 q^{40} - 18 q^{43} - 36 q^{46} - 256 q^{49} - 36 q^{50} - 42 q^{52} + 8 q^{53} + 36 q^{56} - 6 q^{58} + 54 q^{59} - 2 q^{61} - 26 q^{62} - 44 q^{64} + 16 q^{65} - 6 q^{67} + 44 q^{68} - 6 q^{74} + 42 q^{76} - 20 q^{77} - 96 q^{79} + 6 q^{80} - 72 q^{82} + 24 q^{85} + 4 q^{88} + 18 q^{91} + 120 q^{92} + 30 q^{94} - 60 q^{95} - 12 q^{97} + 18 q^{98} + O(q^{100}) \)

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

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