Properties

Label 1200.1.bd
Level $1200$
Weight $1$
Character orbit 1200.bd
Rep. character $\chi_{1200}(443,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $240$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
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 4 0 0 0

Trace form

\( 4q - 4q^{4} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{9} + 4q^{16} + 4q^{19} - 4q^{34} - 4q^{36} - 4q^{46} - 4q^{51} - 4q^{61} - 4q^{64} + 4q^{69} - 4q^{76} + 4q^{81} + 4q^{94} + O(q^{100}) \)

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.bd.a \(2\) \(0.599\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{8}+q^{9}+\cdots\)
1200.1.bd.b \(2\) \(0.599\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots\)