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Properties

Label 833.2.bc
Level $833$
Weight $2$
Character orbit 833.bc
Rep. character $\chi_{833}(31,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $896$
Newform subspaces $6$
Sturm bound $168$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bc (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 6 \)
Sturm bound: \(168\)
Trace bound: \(12\)
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 1472 1024 448
Cusp forms 1216 896 320
Eisenstein series 256 128 128

Trace form

\( 896 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} - 64 q^{8} + 8 q^{9} + O(q^{10}) \) \( 896 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} - 64 q^{8} + 8 q^{9} + 24 q^{10} + 24 q^{12} - 112 q^{15} + 24 q^{17} - 16 q^{18} + 24 q^{19} - 96 q^{22} + 8 q^{23} + 24 q^{24} + 24 q^{26} - 64 q^{29} - 56 q^{30} + 24 q^{31} - 56 q^{32} - 96 q^{36} - 24 q^{37} + 24 q^{38} + 40 q^{39} + 24 q^{40} - 64 q^{43} - 152 q^{44} + 24 q^{45} + 72 q^{46} + 24 q^{47} - 56 q^{51} + 48 q^{52} + 72 q^{53} - 96 q^{54} - 64 q^{57} - 56 q^{58} + 24 q^{59} + 136 q^{60} - 120 q^{61} - 24 q^{65} + 24 q^{66} - 240 q^{68} - 32 q^{71} + 136 q^{72} - 96 q^{73} + 104 q^{74} - 264 q^{75} + 64 q^{78} + 8 q^{79} - 216 q^{80} - 88 q^{81} - 96 q^{82} - 96 q^{85} + 176 q^{86} - 120 q^{87} - 184 q^{88} + 24 q^{89} - 352 q^{92} + 136 q^{93} - 168 q^{94} - 56 q^{95} + 168 q^{96} + 416 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
833.2.bc.a 833.bc 119.s $144$ $6.652$ None 833.2.t.a \(0\) \(-8\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{48}]$
833.2.bc.b 833.bc 119.s $144$ $6.652$ None 833.2.t.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$
833.2.bc.c 833.bc 119.s $144$ $6.652$ None 833.2.t.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$
833.2.bc.d 833.bc 119.s $144$ $6.652$ None 833.2.t.a \(0\) \(8\) \(8\) \(0\) $\mathrm{SU}(2)[C_{48}]$
833.2.bc.e 833.bc 119.s $160$ $6.652$ None 119.2.s.a \(-8\) \(24\) \(24\) \(0\) $\mathrm{SU}(2)[C_{48}]$
833.2.bc.f 833.bc 119.s $160$ $6.652$ None 119.2.p.a \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$

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

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