Properties

Label 3.7.b
Level 3
Weight 7
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(3, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} + O(q^{10}) \) \( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} - 1728q^{12} + 506q^{13} + 4096q^{16} - 10582q^{19} + 7722q^{21} + 15625q^{25} - 19683q^{27} - 18304q^{28} + 35282q^{31} + 46656q^{36} - 89206q^{37} - 13662q^{39} + 111386q^{43} - 110592q^{48} - 35853q^{49} + 32384q^{52} + 285714q^{57} - 420838q^{61} - 208494q^{63} + 262144q^{64} + 172874q^{67} + 638066q^{73} - 421875q^{75} - 677248q^{76} - 204622q^{79} + 531441q^{81} + 494208q^{84} - 144716q^{91} - 952614q^{93} - 56446q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.7.b.a \(1\) \(0.690\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-27\) \(0\) \(-286\) \(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)