Properties

Label 354.3.h
Level 354
Weight 3
Character orbit h
Rep. character \(\chi_{354}(5,\cdot)\)
Character field \(\Q(\zeta_{58})\)
Dimension 1120
Newform subspaces 1
Sturm bound 180
Trace bound 0

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 354.h (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(354, [\chi])\).

Total New Old
Modular forms 3472 1120 2352
Cusp forms 3248 1120 2128
Eisenstein series 224 0 224

Trace form

\( 1120q + 80q^{4} - 8q^{6} - 8q^{7} + 24q^{9} + O(q^{10}) \) \( 1120q + 80q^{4} - 8q^{6} - 8q^{7} + 24q^{9} + 16q^{10} - 34q^{15} - 160q^{16} - 16q^{18} - 24q^{19} + 18q^{21} + 16q^{22} + 16q^{24} + 216q^{25} + 30q^{27} + 16q^{28} + 64q^{30} - 96q^{31} - 76q^{33} - 80q^{34} - 48q^{36} + 200q^{37} + 28q^{39} - 32q^{40} - 48q^{42} + 104q^{43} + 696q^{45} - 32q^{46} - 288q^{49} + 1800q^{51} + 852q^{54} - 360q^{55} + 76q^{57} + 128q^{58} - 280q^{60} + 32q^{61} - 1318q^{63} + 320q^{64} - 1512q^{66} + 344q^{67} - 2640q^{69} - 192q^{70} + 32q^{72} - 40q^{73} - 1014q^{75} + 48q^{76} - 96q^{78} - 32q^{79} - 336q^{81} + 80q^{82} - 36q^{84} - 168q^{85} + 162q^{87} - 32q^{88} - 112q^{90} - 88q^{91} + 316q^{93} + 400q^{94} - 32q^{96} + 184q^{97} + 148q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
354.3.h.a \(1120\) \(9.646\) None \(0\) \(0\) \(0\) \(-8\)

Decomposition of \(S_{3}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)