Properties

Label 1200.1.l
Level $1200$
Weight $1$
Character orbit 1200.l
Rep. character $\chi_{1200}(401,\cdot)$
Character field $\Q$
Dimension $2$
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.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 44 5 39
Cusp forms 8 2 6
Eisenstein series 36 3 33

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{9} + 2q^{19} - 2q^{21} + 2q^{31} + 2q^{39} - 2q^{61} - 4q^{79} + 2q^{81} - 2q^{91} + O(q^{100}) \)

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.l.a \(1\) \(0.599\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-q^{3}+q^{7}+q^{9}-q^{13}+q^{19}-q^{21}+\cdots\)
1200.1.l.b \(1\) \(0.599\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}+q^{13}+q^{19}-q^{21}+\cdots\)

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

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