Properties

Label 833.2.b
Level $833$
Weight $2$
Character orbit 833.b
Rep. character $\chi_{833}(50,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $5$
Sturm bound $168$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(833, [\chi])\).

Total New Old
Modular forms 92 66 26
Cusp forms 76 56 20
Eisenstein series 16 10 6

Trace form

\( 56 q + 4 q^{2} + 56 q^{4} - 52 q^{9} + O(q^{10}) \) \( 56 q + 4 q^{2} + 56 q^{4} - 52 q^{9} + 8 q^{13} + 40 q^{16} - 2 q^{17} - 36 q^{18} - 4 q^{19} - 48 q^{25} - 12 q^{26} + 28 q^{30} - 16 q^{32} + 20 q^{33} - 6 q^{34} - 84 q^{36} + 4 q^{38} - 20 q^{43} + 32 q^{50} + 28 q^{51} + 64 q^{52} - 40 q^{53} + 12 q^{55} - 56 q^{59} + 68 q^{60} + 12 q^{64} - 72 q^{66} - 24 q^{67} + 22 q^{68} - 28 q^{69} - 40 q^{72} + 12 q^{76} + 8 q^{81} + 12 q^{83} + 48 q^{85} + 92 q^{86} + 52 q^{87} + 4 q^{89} + 36 q^{93} + 20 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(833, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
833.2.b.a 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{1}-\beta _{2})q^{4}+\cdots\)
833.2.b.b 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) \(\Q(\sqrt{-119}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{8})q^{4}-\beta _{5}q^{5}+\cdots\)
833.2.b.c 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots\)
833.2.b.d 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots\)
833.2.b.e 833.b 17.b $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-\beta _{1}q^{3}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(833, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(833, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)