Properties

Label 309.1.h
Level $309$
Weight $1$
Character orbit 309.h
Rep. character $\chi_{309}(56,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $34$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 309 = 3 \cdot 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 309.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 309 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(34\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(309, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q - 4q^{3} + 2q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} + 2q^{7} + 4q^{9} + 4q^{10} + 2q^{16} - 2q^{19} - 2q^{21} - 4q^{22} - 4q^{27} - 4q^{30} - 4q^{34} - 2q^{40} - 2q^{43} + 4q^{46} - 2q^{48} - 2q^{55} + 2q^{57} - 2q^{58} + 2q^{63} - 4q^{64} + 4q^{66} - 2q^{67} + 2q^{70} + 8q^{79} + 4q^{81} + 2q^{82} - 2q^{85} + 2q^{88} + 4q^{90} - 4q^{94} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(309, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
309.1.h.a \(4\) \(0.154\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(-4\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{6}+\cdots\)