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Properties

Label 3174.2.p
Level $3174$
Weight $2$
Character orbit 3174.p
Rep. character $\chi_{3174}(5,\cdot)$
Character field $\Q(\zeta_{506})$
Dimension $40480$
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.p (of order \(506\) and degree \(220\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1587 \)
Character field: \(\Q(\zeta_{506})\)
Sturm bound: \(1104\)

Dimensions

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

Total New Old
Modular forms 122320 40480 81840
Cusp forms 120560 40480 80080
Eisenstein series 1760 0 1760

Trace form

\( 40480 q - 4 q^{3} - 184 q^{4} + 42 q^{6} + O(q^{10}) \) \( 40480 q - 4 q^{3} - 184 q^{4} + 42 q^{6} + 4 q^{12} - 8 q^{13} + 22 q^{15} + 184 q^{16} + 28 q^{18} + 66 q^{21} + 4 q^{24} - 52 q^{25} + 38 q^{27} + 44 q^{30} + 16 q^{31} - 116 q^{33} - 46 q^{36} + 136 q^{37} + 24 q^{39} + 44 q^{43} - 76 q^{46} - 4 q^{48} + 268 q^{49} - 138 q^{51} + 8 q^{52} + 6 q^{54} + 120 q^{55} - 158 q^{57} - 36 q^{58} - 22 q^{60} + 4 q^{61} - 110 q^{63} - 184 q^{64} + 96 q^{66} + 232 q^{67} - 128 q^{69} - 32 q^{70} - 28 q^{72} - 44 q^{73} - 152 q^{75} - 82 q^{78} - 88 q^{79} - 52 q^{81} - 136 q^{82} - 22 q^{84} - 28 q^{85} - 112 q^{87} + 230 q^{90} - 8 q^{93} + 48 q^{94} - 4 q^{96} + 132 q^{97} + 296 q^{99} + O(q^{100}) \)

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

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