Properties

Label 1200.1.bj
Level $1200$
Weight $1$
Character orbit 1200.bj
Rep. character $\chi_{1200}(143,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1200.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1200, [\chi])\).

Total New Old
Modular forms 96 12 84
Cusp forms 24 12 12
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 12 0 0 0

Trace form

\( 12q + O(q^{10}) \) \( 12q - 12q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1200.1.bj.a \(4\) \(0.599\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\)
1200.1.bj.b \(8\) \(0.599\) \(\Q(\zeta_{24})\) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)