Properties

Label 345.2.t
Level $345$
Weight $2$
Character orbit 345.t
Rep. character $\chi_{345}(4,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(345, [\chi])\).

Total New Old
Modular forms 520 240 280
Cusp forms 440 240 200
Eisenstein series 80 0 80

Trace form

\( 240q + 28q^{4} - 4q^{5} - 4q^{6} + 24q^{9} + O(q^{10}) \) \( 240q + 28q^{4} - 4q^{5} - 4q^{6} + 24q^{9} + 8q^{14} + 4q^{15} - 36q^{16} - 8q^{19} - 92q^{20} + 8q^{21} + 12q^{24} - 44q^{25} + 32q^{26} - 12q^{29} + 8q^{30} - 20q^{31} - 54q^{34} + 36q^{35} - 28q^{36} - 36q^{39} - 24q^{40} - 28q^{41} - 224q^{44} + 4q^{45} - 8q^{46} + 52q^{49} - 48q^{50} - 18q^{54} - 22q^{55} - 56q^{59} - 36q^{60} + 44q^{61} + 12q^{64} - 16q^{65} + 8q^{66} + 8q^{69} - 152q^{70} + 4q^{71} + 88q^{74} - 8q^{75} - 100q^{76} - 84q^{79} + 122q^{80} - 24q^{81} - 56q^{84} + 186q^{85} - 392q^{86} + 48q^{89} - 304q^{91} + 80q^{94} + 190q^{95} + 16q^{96} + 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(345, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
345.2.t.a \(240\) \(2.755\) None \(0\) \(0\) \(-4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)