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Properties

Label 345.3.k
Level $345$
Weight $3$
Character orbit 345.k
Rep. character $\chi_{345}(208,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 345.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(345, [\chi])\).

Total New Old
Modular forms 200 88 112
Cusp forms 184 88 96
Eisenstein series 16 0 16

Trace form

\( 88q + 8q^{2} + 16q^{5} + 16q^{7} - 24q^{8} + O(q^{10}) \) \( 88q + 8q^{2} + 16q^{5} + 16q^{7} - 24q^{8} - 8q^{10} - 48q^{12} + 56q^{13} - 48q^{15} - 256q^{16} + 24q^{17} + 24q^{18} + 112q^{20} + 48q^{21} + 48q^{22} - 168q^{25} - 304q^{26} - 312q^{28} + 144q^{30} - 88q^{31} - 128q^{32} + 144q^{33} + 168q^{35} + 528q^{36} + 320q^{38} - 416q^{40} + 264q^{41} + 96q^{42} - 128q^{43} - 72q^{45} - 184q^{47} + 192q^{48} + 120q^{50} + 32q^{52} - 288q^{53} + 216q^{55} + 288q^{56} - 48q^{57} - 328q^{58} - 272q^{61} - 128q^{62} + 48q^{63} + 32q^{65} + 144q^{66} + 592q^{67} + 656q^{68} - 152q^{70} + 552q^{71} + 72q^{72} - 192q^{73} + 144q^{75} - 464q^{76} - 88q^{77} - 336q^{78} + 224q^{80} - 792q^{81} + 568q^{82} + 288q^{83} + 296q^{85} - 352q^{86} - 144q^{87} - 312q^{88} + 192q^{90} - 528q^{91} - 896q^{95} - 632q^{97} - 192q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(345, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
345.3.k.a \(88\) \(9.401\) None \(8\) \(0\) \(16\) \(16\)

Decomposition of \(S_{3}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)