Properties

Label 552.1.h
Level $552$
Weight $1$
Character orbit 552.h
Rep. character $\chi_{552}(275,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 552.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 552 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(552, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q - 3q^{6} + O(q^{10}) \) \( 6q - 3q^{6} - 3q^{12} - 3q^{18} + 6q^{25} - 6q^{27} + 3q^{36} - 3q^{48} - 6q^{49} + 6q^{52} - 6q^{58} + 6q^{64} + 3q^{78} + 6q^{82} - 6q^{94} + 3q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(552, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
552.1.h.a \(1\) \(0.275\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
552.1.h.b \(1\) \(0.275\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
552.1.h.c \(2\) \(0.275\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-23}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
552.1.h.d \(2\) \(0.275\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-23}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)