Properties

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

Trace form

\( 880q - 22q^{3} - 44q^{6} - 36q^{7} + O(q^{10}) \) \( 880q - 22q^{3} - 44q^{6} - 36q^{7} - 36q^{10} - 22q^{12} - 28q^{13} - 34q^{15} - 82q^{18} - 52q^{21} - 112q^{22} - 44q^{25} - 34q^{27} - 20q^{28} - 38q^{30} - 72q^{31} - 48q^{33} - 44q^{36} - 84q^{37} - 108q^{40} + 10q^{42} - 12q^{43} - 20q^{45} - 88q^{46} - 94q^{48} - 20q^{51} - 296q^{52} - 20q^{55} + 18q^{57} - 52q^{58} - 42q^{60} - 16q^{61} - 90q^{63} + 60q^{66} - 60q^{67} + 16q^{70} - 58q^{72} - 68q^{73} - 74q^{75} + 72q^{76} + 78q^{78} + 52q^{81} - 60q^{82} - 76q^{85} + 18q^{87} + 12q^{88} - 436q^{90} - 80q^{91} + 12q^{93} + 212q^{96} + 96q^{97} + O(q^{100}) \)

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.x.a \(880\) \(2.755\) None \(0\) \(-22\) \(0\) \(-36\)