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Properties

Label 1110.2.k
Level $1110$
Weight $2$
Character orbit 1110.k
Rep. character $\chi_{1110}(179,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $152$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(i)\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).

Total New Old
Modular forms 472 152 320
Cusp forms 440 152 288
Eisenstein series 32 0 32

Trace form

\( 152 q - 16 q^{9} + O(q^{10}) \) \( 152 q - 16 q^{9} + 8 q^{15} - 152 q^{16} + 16 q^{19} + 72 q^{31} - 16 q^{34} - 16 q^{39} - 16 q^{45} + 32 q^{46} - 120 q^{49} + 40 q^{51} + 40 q^{55} - 8 q^{60} - 48 q^{61} + 48 q^{66} - 16 q^{69} - 16 q^{70} - 20 q^{75} + 16 q^{76} + 24 q^{79} + 48 q^{81} + 20 q^{90} - 16 q^{91} + 24 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)