Properties

Label 354.2.g
Level 354
Weight 2
Character orbit g
Rep. character \(\chi_{354}(11,\cdot)\)
Character field \(\Q(\zeta_{58})\)
Dimension 560
Newforms 2
Sturm bound 120
Trace bound 2

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.g (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Newforms: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(354, [\chi])\).

Total New Old
Modular forms 1792 560 1232
Cusp forms 1568 560 1008
Eisenstein series 224 0 224

Trace form

\( 560q + 2q^{3} - 20q^{4} + 4q^{7} - 6q^{9} + O(q^{10}) \) \( 560q + 2q^{3} - 20q^{4} + 4q^{7} - 6q^{9} + 2q^{12} + 14q^{15} - 20q^{16} + 12q^{19} + 6q^{21} + 8q^{22} - 8q^{25} + 20q^{27} + 4q^{28} - 6q^{36} - 36q^{45} - 16q^{46} + 2q^{48} - 16q^{49} - 236q^{51} - 203q^{54} - 284q^{57} - 160q^{60} - 252q^{63} - 20q^{64} - 203q^{66} - 232q^{69} - 50q^{75} + 12q^{76} - 8q^{78} - 12q^{79} - 14q^{81} + 6q^{84} + 8q^{85} + 30q^{87} + 8q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(354, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
354.2.g.a \(280\) \(2.827\) None \(-10\) \(1\) \(0\) \(2\)
354.2.g.b \(280\) \(2.827\) None \(10\) \(1\) \(0\) \(2\)

Decomposition of \(S_{2}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)