Properties

Label 2268.1.bh
Level $2268$
Weight $1$
Character orbit 2268.bh
Rep. character $\chi_{2268}(1565,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $432$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2268.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(432\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2268, [\chi])\).

Total New Old
Modular forms 82 4 78
Cusp forms 10 4 6
Eisenstein series 72 0 72

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

\( 4q + q^{7} + O(q^{10}) \) \( 4q + q^{7} - q^{13} + 2q^{19} - 2q^{25} - 4q^{31} - q^{37} + 2q^{43} + q^{49} + 2q^{61} + 2q^{67} + 2q^{73} + 2q^{79} - q^{91} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2268.1.bh.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
2268.1.bh.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)