Properties

Label 1260.1.u
Level $1260$
Weight $1$
Character orbit 1260.u
Rep. character $\chi_{1260}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1260.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1260, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 8 8 0
Eisenstein series 32 8 24

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

\( 8 q + O(q^{10}) \) \( 8 q - 8 q^{16} - 8 q^{22} + 8 q^{25} + 8 q^{37} - 8 q^{70} - 8 q^{85} - 8 q^{88} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.1.u.a 1260.u 140.j $4$ $0.629$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-q^{5}+\zeta_{8}q^{7}+\cdots\)
1260.1.u.b 1260.u 140.j $4$ $0.629$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}q^{7}+\cdots\)