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Properties

Label 799.2.k
Level $799$
Weight $2$
Character orbit 799.k
Rep. character $\chi_{799}(18,\cdot)$
Character field $\Q(\zeta_{23})$
Dimension $1408$
Newform subspaces $2$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 799.k (of order \(23\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 47 \)
Character field: \(\Q(\zeta_{23})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(799, [\chi])\).

Total New Old
Modular forms 1628 1408 220
Cusp forms 1540 1408 132
Eisenstein series 88 0 88

Trace form

\( 1408 q - 4 q^{3} - 64 q^{4} - 8 q^{5} - 20 q^{6} - 24 q^{8} - 76 q^{9} + O(q^{10}) \) \( 1408 q - 4 q^{3} - 64 q^{4} - 8 q^{5} - 20 q^{6} - 24 q^{8} - 76 q^{9} - 32 q^{10} - 16 q^{11} - 44 q^{12} - 28 q^{14} - 20 q^{15} - 80 q^{16} - 12 q^{18} - 8 q^{19} - 40 q^{20} - 32 q^{21} - 20 q^{22} - 32 q^{23} - 48 q^{24} - 84 q^{25} - 28 q^{26} - 64 q^{27} - 12 q^{28} - 56 q^{29} - 48 q^{30} - 32 q^{31} - 48 q^{32} - 40 q^{33} - 52 q^{35} + 68 q^{36} - 24 q^{37} + 48 q^{38} + 86 q^{39} + 192 q^{40} + 74 q^{41} - 76 q^{42} + 2 q^{43} - 88 q^{44} - 148 q^{45} + 144 q^{46} - 2 q^{47} - 152 q^{48} - 70 q^{49} + 88 q^{50} - 88 q^{52} - 22 q^{53} - 136 q^{54} + 54 q^{55} + 168 q^{56} + 66 q^{57} - 20 q^{58} - 84 q^{59} + 80 q^{60} - 48 q^{61} - 132 q^{62} - 52 q^{63} - 216 q^{64} - 84 q^{65} - 120 q^{66} - 48 q^{67} - 124 q^{69} - 192 q^{70} - 84 q^{71} - 164 q^{72} - 36 q^{73} - 64 q^{74} - 72 q^{75} - 140 q^{76} - 84 q^{77} - 200 q^{78} - 28 q^{79} - 248 q^{80} + 92 q^{81} + 230 q^{82} + 32 q^{83} + 52 q^{84} - 4 q^{85} + 296 q^{86} + 84 q^{87} - 156 q^{88} - 64 q^{89} + 484 q^{90} + 368 q^{91} + 246 q^{92} - 140 q^{93} - 144 q^{94} - 92 q^{95} - 116 q^{96} - 40 q^{97} + 154 q^{98} + 344 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(799, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
799.2.k.a 799.k 47.c $704$ $6.380$ None \(0\) \(-2\) \(-6\) \(21\) $\mathrm{SU}(2)[C_{23}]$
799.2.k.b 799.k 47.c $704$ $6.380$ None \(0\) \(-2\) \(-2\) \(-21\) $\mathrm{SU}(2)[C_{23}]$

Decomposition of \(S_{2}^{\mathrm{old}}(799, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(799, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(47, [\chi])\)\(^{\oplus 2}\)