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Properties

Label 756.2.n
Level $756$
Weight $2$
Character orbit 756.n
Rep. character $\chi_{756}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 312 104 208
Cusp forms 264 88 176
Eisenstein series 48 16 32

Trace form

\( 88 q - q^{2} + q^{4} + 8 q^{8} + O(q^{10}) \) \( 88 q - q^{2} + q^{4} + 8 q^{8} - 6 q^{10} + 15 q^{14} + q^{16} + 12 q^{17} - 24 q^{20} + 2 q^{22} - 60 q^{25} + 12 q^{26} - q^{32} + 6 q^{34} - 4 q^{37} + 5 q^{44} + 2 q^{46} - 2 q^{49} + 31 q^{50} + 4 q^{53} + 48 q^{56} + 6 q^{58} - 6 q^{61} - 8 q^{64} - 14 q^{65} + 8 q^{70} - 12 q^{73} - 34 q^{74} - 12 q^{76} - 62 q^{77} - 51 q^{80} - 12 q^{82} - 14 q^{85} + 26 q^{86} + 14 q^{88} + 72 q^{89} - 44 q^{92} - 3 q^{94} + 5 q^{98} + O(q^{100}) \)

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.n.a 756.n 252.n $4$ $6.037$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots\)
756.2.n.b 756.n 252.n $84$ $6.037$ None \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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