Properties

Label 1352.1.p
Level $1352$
Weight $1$
Character orbit 1352.p
Rep. character $\chi_{1352}(147,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $3$
Sturm bound $182$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1352 = 2^{3} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1352.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(182\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1352, [\chi])\).

Total New Old
Modular forms 44 36 8
Cusp forms 16 16 0
Eisenstein series 28 20 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 2 q^{10} - 4 q^{14} - 8 q^{16} + 2 q^{22} - 12 q^{25} - 4 q^{27} - 2 q^{30} - 2 q^{35} + 4 q^{36} + 4 q^{38} - 4 q^{40} - 2 q^{42} + 4 q^{48} + 6 q^{49} + 12 q^{51} + 2 q^{56} - 4 q^{62} - 8 q^{64} - 8 q^{66} + 4 q^{68} + 2 q^{74} - 2 q^{75} - 2 q^{82} - 2 q^{88} + 2 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1352.1.p.a 1352.p 104.p $2$ $0.675$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(-1\) \(1\) \(-2\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1352.1.p.b 1352.p 104.p $2$ $0.675$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(1\) \(1\) \(2\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1352.1.p.c 1352.p 104.p $12$ $0.675$ 12.0.\(\cdots\).1 $D_{7}$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots\)