Properties

Label 354.2.c
Level 354
Weight 2
Character orbit c
Rep. character \(\chi_{354}(353,\cdot)\)
Character field \(\Q\)
Dimension 20
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 177 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 64 20 44
Cusp forms 56 20 36
Eisenstein series 8 0 8

Trace form

\( 20q - 2q^{3} + 20q^{4} - 4q^{7} + 6q^{9} + O(q^{10}) \) \( 20q - 2q^{3} + 20q^{4} - 4q^{7} + 6q^{9} - 2q^{12} - 14q^{15} + 20q^{16} - 12q^{19} - 6q^{21} - 8q^{22} + 8q^{25} - 20q^{27} - 4q^{28} + 6q^{36} - 22q^{45} + 16q^{46} - 2q^{48} + 16q^{49} + 4q^{51} - 6q^{57} - 14q^{60} - 38q^{63} + 20q^{64} - 8q^{75} - 12q^{76} + 8q^{78} + 12q^{79} + 14q^{81} - 6q^{84} - 8q^{85} - 30q^{87} - 8q^{88} + O(q^{100}) \)

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.c.a \(10\) \(2.827\) 10.0.\(\cdots\).1 None \(-10\) \(-1\) \(0\) \(-2\) \(q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
354.2.c.b \(10\) \(2.827\) 10.0.\(\cdots\).1 None \(10\) \(-1\) \(0\) \(-2\) \(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots\)

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

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