Properties

Label 2268.1.h
Level $2268$
Weight $1$
Character orbit 2268.h
Rep. character $\chi_{2268}(2267,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $432$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2268.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(432\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 52 16 36
Cusp forms 28 8 20
Eisenstein series 24 8 16

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

\( 8q + O(q^{10}) \) \( 8q + 4q^{16} + 4q^{22} - 8q^{25} - 4q^{28} - 4q^{46} - 8q^{49} - 4q^{58} - 4q^{88} + O(q^{100}) \)

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.h.a \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)