Properties

Label 756.1.d
Level $756$
Weight $1$
Character orbit 756.d
Rep. character $\chi_{756}(433,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 756.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(756, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 10 4 6
Eisenstein series 18 0 18

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - q^{7} + O(q^{10}) \) \( 4 q - q^{7} - 2 q^{25} + 4 q^{37} - 2 q^{43} + q^{49} + 2 q^{67} - 4 q^{79} - 6 q^{85} - 3 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
756.1.d.a 756.d 7.b $2$ $0.377$ \(\Q(\sqrt{-3}) \) $D_{6}$ None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-2\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+\cdots\)
756.1.d.b 756.d 7.b $2$ $0.377$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(\zeta_{6}+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)