Properties

Label 819.2.y
Level $819$
Weight $2$
Character orbit 819.y
Rep. character $\chi_{819}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $9$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 9 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 240 100 140
Cusp forms 208 92 116
Eisenstein series 32 8 24

Trace form

\( 92 q + 4 q^{2} - 4 q^{8} + O(q^{10}) \) \( 92 q + 4 q^{2} - 4 q^{8} - 8 q^{11} + 16 q^{14} - 112 q^{16} - 16 q^{22} + 28 q^{28} - 4 q^{29} - 24 q^{32} + 20 q^{35} - 36 q^{37} - 28 q^{44} - 40 q^{46} - 12 q^{50} + 68 q^{53} - 12 q^{58} + 24 q^{65} - 20 q^{67} - 20 q^{70} - 24 q^{71} + 80 q^{74} + 28 q^{79} - 100 q^{85} - 84 q^{86} - 16 q^{91} - 200 q^{92} - 92 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
819.2.y.a 819.y 91.i $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+2\beta _{2})q^{5}+\cdots\)
819.2.y.b 819.y 91.i $4$ $6.540$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
819.2.y.c 819.y 91.i $4$ $6.540$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
819.2.y.d 819.y 91.i $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(8\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
819.2.y.e 819.y 91.i $8$ $6.540$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{6})q^{7}+\cdots\)
819.2.y.f 819.y 91.i $12$ $6.540$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+(-1+\cdots)q^{5}+\cdots\)
819.2.y.g 819.y 91.i $12$ $6.540$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(12\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+(1+\cdots)q^{5}+\cdots\)
819.2.y.h 819.y 91.i $12$ $6.540$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}+(\beta _{4}-\beta _{6}-\beta _{7}-\beta _{8})q^{4}+\cdots\)
819.2.y.i 819.y 91.i $32$ $6.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)