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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
345.2.x.a 345.x 345.x $880$ $2.755$ None \(0\) \(-22\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{44}]$