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Properties

Label 756.2.be
Level $756$
Weight $2$
Character orbit 756.be
Rep. character $\chi_{756}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $5$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 312 128 184
Cusp forms 264 128 136
Eisenstein series 48 0 48

Trace form

\( 128 q + O(q^{10}) \) \( 128 q - 8 q^{13} + 16 q^{16} - 20 q^{22} + 60 q^{25} + 22 q^{28} + 8 q^{34} - 4 q^{37} + 26 q^{40} - 6 q^{46} + 8 q^{49} + 26 q^{52} - 12 q^{58} + 8 q^{61} - 60 q^{64} + 78 q^{70} + 4 q^{73} - 144 q^{76} + 74 q^{82} + 16 q^{85} - 40 q^{88} - 30 q^{94} + 88 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
756.2.be.a 756.be 84.n $4$ $6.037$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
756.2.be.b 756.be 84.n $4$ $6.037$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{1}q^{5}+(1+2\beta _{2}+\cdots)q^{7}+\cdots\)
756.2.be.c 756.be 84.n $28$ $6.037$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
756.2.be.d 756.be 84.n $28$ $6.037$ None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$
756.2.be.e 756.be 84.n $64$ $6.037$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)