Properties

Label 3174.2.j
Level $3174$
Weight $2$
Character orbit 3174.j
Rep. character $\chi_{3174}(137,\cdot)$
Character field $\Q(\zeta_{46})$
Dimension $4048$
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.j (of order \(46\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1587 \)
Character field: \(\Q(\zeta_{46})\)
Sturm bound: \(1104\)

Dimensions

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

Total New Old
Modular forms 12232 4048 8184
Cusp forms 12056 4048 8008
Eisenstein series 176 0 176

Trace form

\( 4048 q + 4 q^{3} + 184 q^{4} - 42 q^{6} + O(q^{10}) \) \( 4048 q + 4 q^{3} + 184 q^{4} - 42 q^{6} - 4 q^{12} + 8 q^{13} - 184 q^{16} + 16 q^{18} - 4 q^{24} + 52 q^{25} + 28 q^{27} - 16 q^{31} + 138 q^{33} + 46 q^{36} - 92 q^{37} - 24 q^{39} + 76 q^{46} + 4 q^{48} - 136 q^{49} + 138 q^{51} - 8 q^{52} - 28 q^{54} - 120 q^{55} + 92 q^{57} - 8 q^{58} - 92 q^{61} + 184 q^{64} - 184 q^{66} - 276 q^{67} + 18 q^{69} + 32 q^{70} - 16 q^{72} + 20 q^{75} + 16 q^{78} + 8 q^{81} + 92 q^{82} - 16 q^{85} + 178 q^{87} - 230 q^{90} + 8 q^{93} - 48 q^{94} + 4 q^{96} - 230 q^{99} + O(q^{100}) \)

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

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