Properties

Label 3240.1.p
Level $3240$
Weight $1$
Character orbit 3240.p
Rep. character $\chi_{3240}(1459,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $648$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3240.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(648\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3240, [\chi])\).

Total New Old
Modular forms 46 16 30
Cusp forms 22 8 14
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 8 0 0 0

Trace form

\( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} + 8 q^{16} + 8 q^{25} + 8 q^{49} + 8 q^{64} - 8 q^{91} - 8 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3240.1.p.a 3240.p 40.e $1$ $1.617$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
3240.1.p.b 3240.p 40.e $1$ $1.617$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(-1\) \(0\) \(-1\) \(1\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
3240.1.p.c 3240.p 40.e $1$ $1.617$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3240.1.p.d 3240.p 40.e $1$ $1.617$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(1\) \(0\) \(1\) \(1\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
3240.1.p.e 3240.p 40.e $2$ $1.617$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.e \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots\)
3240.1.p.f 3240.p 40.e $2$ $1.617$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.e \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)