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Properties

Label 3174.2.d
Level $3174$
Weight $2$
Character orbit 3174.d
Rep. character $\chi_{3174}(3173,\cdot)$
Character field $\Q$
Dimension $168$
Sturm bound $1104$

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Defining parameters

Level: \( N \) \(=\) \( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3174.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(1104\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3174, [\chi])\).

Total New Old
Modular forms 600 168 432
Cusp forms 504 168 336
Eisenstein series 96 0 96

Trace form

\( 168 q + 4 q^{3} - 168 q^{4} + 4 q^{6} + O(q^{10}) \) \( 168 q + 4 q^{3} - 168 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} + 168 q^{16} + 16 q^{18} - 4 q^{24} + 128 q^{25} + 28 q^{27} - 16 q^{31} - 24 q^{39} + 4 q^{48} - 120 q^{49} - 8 q^{52} - 28 q^{54} + 64 q^{55} - 8 q^{58} - 168 q^{64} + 16 q^{70} - 16 q^{72} + 16 q^{73} - 12 q^{75} + 16 q^{78} - 24 q^{81} - 32 q^{85} + 72 q^{87} + 8 q^{93} - 64 q^{94} + 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3174, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3174, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3174, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1587, [\chi])\)\(^{\oplus 2}\)