Properties

Label 819.2.c
Level $819$
Weight $2$
Character orbit 819.c
Rep. character $\chi_{819}(64,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $5$
Sturm bound $224$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 120 34 86
Cusp forms 104 34 70
Eisenstein series 16 0 16

Trace form

\( 34 q - 32 q^{4} + O(q^{10}) \) \( 34 q - 32 q^{4} + 8 q^{10} - 4 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 8 q^{22} - 2 q^{23} - 28 q^{25} - 32 q^{26} + 26 q^{29} + 10 q^{35} - 52 q^{38} - 44 q^{40} + 38 q^{43} - 34 q^{49} + 56 q^{52} + 26 q^{53} - 36 q^{55} - 12 q^{56} + 4 q^{61} + 40 q^{62} + 44 q^{64} - 22 q^{65} + 20 q^{68} - 72 q^{74} - 22 q^{79} - 96 q^{82} - 24 q^{88} - 10 q^{91} + 20 q^{92} + 20 q^{94} + 10 q^{95} + O(q^{100}) \)

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.c.a 819.c 13.b $2$ $6.540$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+3iq^{5}+iq^{7}-6q^{10}+\cdots\)
819.2.c.b 819.c 13.b $6$ $6.540$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.c.c 819.c 13.b $6$ $6.540$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
819.2.c.d 819.c 13.b $8$ $6.540$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots\)
819.2.c.e 819.c 13.b $12$ $6.540$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-1+\beta _{10})q^{4}-\beta _{1}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)