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Properties

Label 1872.4.bp
Level $1872$
Weight $4$
Character orbit 1872.bp
Rep. character $\chi_{1872}(1061,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $672$
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.bp (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
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 672 1360
Cusp forms 2000 672 1328
Eisenstein series 32 0 32

Trace form

\( 672 q + O(q^{10}) \) \( 672 q - 144 q^{10} + 432 q^{22} + 16800 q^{25} - 72 q^{28} + 360 q^{34} + 3120 q^{40} + 864 q^{43} + 2280 q^{46} + 120 q^{52} + 2448 q^{58} - 3744 q^{64} + 1032 q^{70} - 4440 q^{76} - 3312 q^{82} - 3600 q^{91} + 9360 q^{94} + O(q^{100}) \)

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

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