Properties

Label 345.2.s
Level $345$
Weight $2$
Character orbit 345.s
Rep. character $\chi_{345}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
Newform subspaces $2$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.s (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 520 320 200
Cusp forms 440 320 120
Eisenstein series 80 0 80

Trace form

\( 320q + 28q^{4} - 2q^{6} + 4q^{9} + O(q^{10}) \) \( 320q + 28q^{4} - 2q^{6} + 4q^{9} - 6q^{12} + 4q^{16} + 22q^{18} - 66q^{21} - 132q^{24} - 32q^{25} - 54q^{27} + 16q^{31} - 22q^{34} - 58q^{36} - 8q^{39} - 154q^{40} - 88q^{43} - 164q^{46} + 46q^{48} - 68q^{49} + 4q^{52} - 30q^{54} - 28q^{55} + 66q^{57} - 4q^{58} + 44q^{61} + 110q^{63} - 16q^{64} + 88q^{66} + 44q^{67} + 20q^{69} + 24q^{70} + 208q^{72} + 20q^{73} + 88q^{76} - 186q^{78} + 44q^{79} + 56q^{81} + 140q^{82} - 242q^{84} + 16q^{85} - 232q^{87} - 284q^{93} - 60q^{94} + 26q^{96} - 264q^{99} + O(q^{100}) \)

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.s.a \(160\) \(2.755\) None \(0\) \(0\) \(-16\) \(0\)
345.2.s.b \(160\) \(2.755\) None \(0\) \(0\) \(16\) \(0\)

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

\( S_{2}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)