Properties

Label 676.1.i
Level $676$
Weight $1$
Character orbit 676.i
Rep. character $\chi_{676}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $91$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 676.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(91\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(676, [\chi])\).

Total New Old
Modular forms 32 24 8
Cusp forms 4 4 0
Eisenstein series 28 20 8

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

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

Trace form

\( 4 q + 2 q^{4} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} - 2 q^{9} - 2 q^{10} - 2 q^{16} - 2 q^{17} + 2 q^{29} + 2 q^{36} - 4 q^{40} + 2 q^{49} - 4 q^{53} + 2 q^{61} - 4 q^{64} + 2 q^{68} + 2 q^{74} - 2 q^{81} - 2 q^{82} + 4 q^{90} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(676, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
676.1.i.a \(4\) \(0.337\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)