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Properties

Label 833.2.v
Level $833$
Weight $2$
Character orbit 833.v
Rep. character $\chi_{833}(128,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $448$
Newform subspaces $8$
Sturm bound $168$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.v (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 8 \)
Sturm bound: \(168\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 736 512 224
Cusp forms 608 448 160
Eisenstein series 128 64 64

Trace form

\( 448 q + 4 q^{2} + 4 q^{3} + 16 q^{6} - 16 q^{8} + 4 q^{9} + O(q^{10}) \) \( 448 q + 4 q^{2} + 4 q^{3} + 16 q^{6} - 16 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 28 q^{12} - 88 q^{15} + 184 q^{16} - 4 q^{17} + 24 q^{18} + 4 q^{19} + 48 q^{20} - 8 q^{23} + 28 q^{24} + 8 q^{25} - 36 q^{26} + 64 q^{27} - 32 q^{29} + 4 q^{31} - 40 q^{33} + 16 q^{34} - 16 q^{36} + 52 q^{37} - 24 q^{39} - 28 q^{40} - 40 q^{41} - 96 q^{43} - 108 q^{44} - 8 q^{45} + 4 q^{46} - 56 q^{48} - 192 q^{50} - 52 q^{51} + 24 q^{52} - 76 q^{53} - 24 q^{54} - 32 q^{57} - 44 q^{58} - 4 q^{59} - 156 q^{60} + 24 q^{61} - 88 q^{62} - 12 q^{66} + 60 q^{68} - 192 q^{69} - 48 q^{71} + 24 q^{73} + 164 q^{74} + 108 q^{75} + 8 q^{76} + 16 q^{78} + 20 q^{79} + 44 q^{80} - 24 q^{82} + 88 q^{83} + 24 q^{85} - 104 q^{86} - 68 q^{87} - 152 q^{88} + 48 q^{90} + 144 q^{92} + 8 q^{93} - 44 q^{94} - 64 q^{95} + 12 q^{96} - 80 q^{97} - 320 q^{99} + O(q^{100}) \)

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.v.a 833.v 119.q $8$ $6.652$ \(\Q(\zeta_{24})\) None \(4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$ \(q+(1+\zeta_{24}^{2}-\zeta_{24}^{3}-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+\cdots\)
833.2.v.b 833.v 119.q $8$ $6.652$ \(\Q(\zeta_{24})\) None \(4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$ \(q+(1+\zeta_{24}^{2}-\zeta_{24}^{3}-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+\cdots\)
833.2.v.c 833.v 119.q $64$ $6.652$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$
833.2.v.d 833.v 119.q $64$ $6.652$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$
833.2.v.e 833.v 119.q $64$ $6.652$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$
833.2.v.f 833.v 119.q $80$ $6.652$ None \(-4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$
833.2.v.g 833.v 119.q $80$ $6.652$ None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{24}]$
833.2.v.h 833.v 119.q $80$ $6.652$ None \(0\) \(4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{24}]$

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

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