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Properties

Label 833.2.e
Level $833$
Weight $2$
Character orbit 833.e
Rep. character $\chi_{833}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
Newform subspaces $12$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 184 108 76
Cusp forms 152 108 44
Eisenstein series 32 0 32

Trace form

\( 108 q + 4 q^{2} + 2 q^{3} - 52 q^{4} + 4 q^{5} - 12 q^{8} - 60 q^{9} + O(q^{10}) \) \( 108 q + 4 q^{2} + 2 q^{3} - 52 q^{4} + 4 q^{5} - 12 q^{8} - 60 q^{9} - 6 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} - 24 q^{15} - 32 q^{16} + 4 q^{17} + 32 q^{18} - 6 q^{19} - 48 q^{20} - 40 q^{22} + 32 q^{23} - 62 q^{25} - 8 q^{26} - 16 q^{27} - 24 q^{29} + 32 q^{30} + 6 q^{31} + 36 q^{32} - 26 q^{33} - 8 q^{34} + 112 q^{36} - 18 q^{37} - 30 q^{38} - 20 q^{39} - 32 q^{40} + 12 q^{41} + 36 q^{43} + 14 q^{44} + 4 q^{45} + 12 q^{46} - 2 q^{47} - 52 q^{48} - 40 q^{50} + 2 q^{52} + 8 q^{53} + 28 q^{54} + 28 q^{55} + 24 q^{57} + 56 q^{58} - 2 q^{59} + 56 q^{60} - 36 q^{62} - 92 q^{64} + 26 q^{65} - 4 q^{67} + 12 q^{68} - 56 q^{69} + 28 q^{71} + 64 q^{72} + 28 q^{73} - 8 q^{74} - 12 q^{75} + 44 q^{76} + 20 q^{78} - 8 q^{79} - 10 q^{80} - 74 q^{81} + 40 q^{82} - 24 q^{83} - 64 q^{86} + 2 q^{87} + 52 q^{88} - 24 q^{89} - 92 q^{90} + 16 q^{92} - 14 q^{93} - 26 q^{94} + 60 q^{95} + 24 q^{96} + 28 q^{97} - 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.e.a 833.e 7.c $2$ $6.652$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.b 833.e 7.c $2$ $6.652$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.c 833.e 7.c $6$ $6.652$ 6.0.64827.1 None \(1\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.d 833.e 7.c $8$ $6.652$ 8.0.310217769.2 None \(1\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
833.2.e.e 833.e 7.c $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{3}+\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.f 833.e 7.c $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{7})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.g 833.e 7.c $8$ $6.652$ 8.0.310217769.2 None \(1\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
833.2.e.h 833.e 7.c $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{3}-\beta _{7}-\beta _{8})q^{3}+(\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
833.2.e.i 833.e 7.c $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{7}+\beta _{8})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
833.2.e.j 833.e 7.c $14$ $6.652$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{13}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.k 833.e 7.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(-8\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{6}+\beta _{10}+\beta _{14}+\cdots)q^{3}+\cdots\)
833.2.e.l 833.e 7.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(8\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{6}-\beta _{10}-\beta _{14})q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(833, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)