Properties

Label 735.2.v
Level 735
Weight 2
Character orbit v
Rep. character \(\chi_{735}(178,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 160
Newform subspaces 4
Sturm bound 224
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

Total New Old
Modular forms 512 160 352
Cusp forms 384 160 224
Eisenstein series 128 0 128

Trace form

\( 160q + 12q^{5} + 24q^{8} + O(q^{10}) \) \( 160q + 12q^{5} + 24q^{8} + 12q^{10} + 8q^{11} + 8q^{15} + 96q^{16} + 24q^{22} - 20q^{25} - 24q^{26} - 16q^{30} - 24q^{31} - 24q^{32} + 36q^{33} - 160q^{36} + 4q^{37} - 12q^{38} - 12q^{40} - 56q^{43} + 88q^{46} + 60q^{47} - 72q^{50} + 8q^{51} + 108q^{52} - 64q^{53} - 32q^{57} - 108q^{58} - 20q^{60} + 24q^{61} + 20q^{65} - 72q^{66} - 24q^{67} - 132q^{68} - 16q^{71} - 12q^{72} - 36q^{73} - 48q^{75} - 128q^{78} + 12q^{80} + 80q^{81} - 12q^{82} + 88q^{85} + 48q^{86} + 24q^{87} + 32q^{88} + 120q^{92} + 48q^{93} - 4q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
735.2.v.a \(32\) \(5.869\) None \(0\) \(0\) \(0\) \(0\)
735.2.v.b \(32\) \(5.869\) None \(0\) \(0\) \(12\) \(0\)
735.2.v.c \(48\) \(5.869\) None \(0\) \(0\) \(-8\) \(0\)
735.2.v.d \(48\) \(5.869\) None \(0\) \(0\) \(8\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database