Properties

Label 735.1.f
Level $735$
Weight $1$
Character orbit 735.f
Rep. character $\chi_{735}(344,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 735.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(735, [\chi])\).

Total New Old
Modular forms 22 16 6
Cusp forms 6 6 0
Eisenstein series 16 10 6

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

\( 6 q + 2 q^{4} + 6 q^{9} - 2 q^{15} - 2 q^{16} + 6 q^{25} + 2 q^{36} - 8 q^{46} - 4 q^{51} - 6 q^{60} - 6 q^{64} - 4 q^{79} + 6 q^{81} - 4 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
735.1.f.a 735.f 15.d $1$ $0.367$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) 735.1.f.a \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots\)
735.1.f.b 735.f 15.d $1$ $0.367$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) 735.1.f.a \(0\) \(1\) \(1\) \(0\) \(q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots\)
735.1.f.c 735.f 15.d $2$ $0.367$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-15}) \) None 735.1.f.c \(0\) \(-2\) \(2\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots\)
735.1.f.d 735.f 15.d $2$ $0.367$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-15}) \) None 735.1.f.c \(0\) \(2\) \(-2\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots\)