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Properties

Label 1872.2.bk
Level $1872$
Weight $2$
Character orbit 1872.bk
Rep. character $\chi_{1872}(755,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 688 192 496
Cusp forms 656 192 464
Eisenstein series 32 0 32

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 16 q^{10} + 32 q^{16} - 32 q^{19} + 16 q^{22} - 48 q^{34} - 64 q^{40} + 32 q^{43} - 16 q^{46} + 192 q^{49} - 16 q^{52} + 64 q^{55} - 48 q^{58} + 64 q^{61} + 96 q^{64} + 32 q^{67} + 48 q^{70} + 64 q^{76} + 64 q^{85} - 192 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)