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Properties

Label 1872.4.ey
Level $1872$
Weight $4$
Character orbit 1872.ey
Rep. character $\chi_{1872}(829,\cdot)$
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.ey (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

\( 1672 q + 6 q^{2} - 2 q^{4} + O(q^{10}) \) \( 1672 q + 6 q^{2} - 2 q^{4} - 2 q^{10} + 6 q^{11} - 4 q^{13} - 232 q^{14} - 2 q^{16} + 4 q^{17} - 6 q^{19} - 114 q^{20} - 470 q^{22} - 288 q^{26} + 456 q^{28} + 2 q^{29} - 414 q^{32} + 252 q^{35} - 6 q^{37} + 228 q^{38} - 2388 q^{40} + 430 q^{43} - 1056 q^{46} - 39792 q^{49} - 2172 q^{50} + 2462 q^{52} + 8 q^{53} + 1188 q^{56} - 6 q^{58} - 2058 q^{59} - 2 q^{61} + 1930 q^{62} + 532 q^{64} - 480 q^{65} - 6 q^{67} - 284 q^{68} + 3722 q^{74} + 2154 q^{76} - 1364 q^{77} + 6304 q^{79} + 6 q^{80} - 3012 q^{82} + 744 q^{85} + 756 q^{88} + 4178 q^{91} + 6504 q^{92} + 2146 q^{94} + 6084 q^{95} - 12 q^{97} - 5994 q^{98} + O(q^{100}) \)

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

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