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

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

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1200.1.bd.a 1200.bd 240.ad $2$ $0.599$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{8}+q^{9}+\cdots\)
1200.1.bd.b 1200.bd 240.ad $2$ $0.599$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots\)