Properties

Label 345.3.e
Level $345$
Weight $3$
Character orbit 345.e
Rep. character $\chi_{345}(116,\cdot)$
Character field $\Q$
Dimension $60$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 100 60 40
Cusp forms 92 60 32
Eisenstein series 8 0 8

Trace form

\( 60q + 8q^{3} - 128q^{4} - 22q^{6} + 24q^{7} + 20q^{9} + O(q^{10}) \) \( 60q + 8q^{3} - 128q^{4} - 22q^{6} + 24q^{7} + 20q^{9} - 38q^{12} - 64q^{13} + 20q^{15} + 288q^{16} + 90q^{18} - 24q^{19} - 28q^{21} + 120q^{22} - 36q^{24} - 300q^{25} - 88q^{27} - 248q^{28} + 80q^{30} + 152q^{31} - 64q^{33} - 24q^{34} - 126q^{36} + 76q^{39} + 176q^{42} - 32q^{43} + 326q^{48} + 524q^{49} - 20q^{51} + 188q^{52} - 436q^{54} - 112q^{57} - 180q^{58} - 20q^{60} - 224q^{61} + 384q^{63} - 116q^{64} - 564q^{66} - 520q^{67} - 120q^{70} + 60q^{72} + 464q^{73} - 40q^{75} + 176q^{76} + 422q^{78} - 24q^{79} + 316q^{81} - 148q^{82} + 264q^{84} - 120q^{85} - 452q^{87} - 392q^{88} + 180q^{90} + 568q^{91} + 292q^{93} - 364q^{94} - 378q^{96} + 464q^{97} - 488q^{99} + O(q^{100}) \)

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.e.a \(60\) \(9.401\) None \(0\) \(8\) \(0\) \(24\)

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

\( S_{3}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)