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Properties

Label 783.2.m
Level $783$
Weight $2$
Character orbit 783.m
Rep. character $\chi_{783}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 783 = 3^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 783.m (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 261 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(783, [\chi])\).

Total New Old
Modular forms 384 128 256
Cusp forms 336 112 224
Eisenstein series 48 16 32

Trace form

\( 112 q + 6 q^{2} - 4 q^{7} + O(q^{10}) \) \( 112 q + 6 q^{2} - 4 q^{7} - 6 q^{11} + 18 q^{14} + 40 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{23} - 44 q^{25} + 42 q^{29} - 2 q^{31} + 66 q^{32} - 8 q^{37} - 12 q^{40} + 18 q^{41} - 2 q^{43} + 8 q^{46} - 36 q^{49} - 24 q^{50} - 36 q^{52} + 36 q^{55} - 84 q^{56} + 28 q^{58} - 48 q^{59} - 14 q^{61} - 24 q^{65} + 102 q^{68} - 8 q^{73} - 144 q^{74} + 14 q^{76} + 72 q^{77} - 2 q^{79} + 80 q^{82} + 120 q^{83} - 48 q^{85} - 36 q^{88} - 40 q^{94} - 204 q^{95} + 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(783, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
783.2.m.a 783.m 261.l $112$ $6.252$ None 261.2.l.a \(6\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(783, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(783, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)