Properties

Label 345.2.w
Level $345$
Weight $2$
Character orbit 345.w
Rep. character $\chi_{345}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $480$
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.w (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
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 1040 480 560
Cusp forms 880 480 400
Eisenstein series 160 0 160

Trace form

\( 480q + 8q^{6} + O(q^{10}) \) \( 480q + 8q^{6} + 8q^{13} + 72q^{16} - 96q^{23} - 24q^{25} - 16q^{26} - 176q^{28} + 8q^{31} + 40q^{32} - 8q^{35} - 56q^{36} - 88q^{37} - 40q^{41} - 220q^{42} + 56q^{46} - 152q^{47} + 32q^{48} + 128q^{50} - 220q^{52} - 48q^{55} - 88q^{57} + 32q^{58} - 88q^{61} - 96q^{62} - 112q^{70} + 24q^{71} - 40q^{73} + 32q^{75} - 176q^{76} - 40q^{77} + 16q^{78} - 396q^{80} + 48q^{81} + 88q^{82} - 400q^{85} - 8q^{87} - 104q^{92} + 64q^{93} - 244q^{95} - 48q^{96} + 200q^{98} + O(q^{100}) \)

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.w.a \(480\) \(2.755\) None \(0\) \(0\) \(0\) \(0\)

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

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