Properties

Label 2268.1.s
Level $2268$
Weight $1$
Character orbit 2268.s
Rep. character $\chi_{2268}(755,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $7$
Sturm bound $432$
Trace bound $28$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2268.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(28\)

Dimensions

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

Total New Old
Modular forms 80 40 40
Cusp forms 32 32 0
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32q - 4q^{4} + O(q^{10}) \) \( 32q - 4q^{4} - 4q^{16} + 4q^{22} + 12q^{25} - 8q^{37} - 8q^{46} + 8q^{49} + 8q^{64} + 4q^{70} + 8q^{85} + 4q^{88} + O(q^{100}) \)

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.s.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.c \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.d \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.e \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.f \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.g \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(D_{4}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)