Properties

Label 2268.1.bc
Level $2268$
Weight $1$
Character orbit 2268.bc
Rep. character $\chi_{2268}(433,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
Sturm bound $432$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2268.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 110 8 102
Cusp forms 38 8 30
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 8 0 0 0

Trace form

\( 8q + q^{7} + O(q^{10}) \) \( 8q + q^{7} + 2q^{25} + 8q^{37} + 2q^{43} - q^{49} - 2q^{67} + 4q^{79} + 6q^{85} - 6q^{91} + O(q^{100}) \)

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.bc.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{6}\) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(-3\) \(1\) \(q+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
2268.1.bc.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(1-\zeta_{6}^{2})q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.c \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.d \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{6}\) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(3\) \(1\) \(q+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)

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

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