Properties

Label 2683.2.a
Level $2683$
Weight $2$
Character orbit 2683.a
Rep. character $\chi_{2683}(1,\cdot)$
Character field $\Q$
Dimension $223$
Newform subspaces $2$
Sturm bound $447$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2683 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2683.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(447\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2683))\).

Total New Old
Modular forms 224 224 0
Cusp forms 223 223 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2683\)Dim
\(+\)\(107\)
\(-\)\(116\)

Trace form

\( 223 q - 2 q^{2} - 2 q^{3} + 222 q^{4} - 4 q^{7} + 219 q^{9} + O(q^{10}) \) \( 223 q - 2 q^{2} - 2 q^{3} + 222 q^{4} - 4 q^{7} + 219 q^{9} + 12 q^{10} - 6 q^{12} - 2 q^{13} - 10 q^{14} + 10 q^{15} + 216 q^{16} - 8 q^{17} - 6 q^{18} - 2 q^{19} - 4 q^{20} - 24 q^{21} - 4 q^{22} - 2 q^{23} + 12 q^{24} + 241 q^{25} + 6 q^{26} + 4 q^{27} - 6 q^{29} + 30 q^{30} - 8 q^{31} - 2 q^{32} - 24 q^{33} + 8 q^{34} + 222 q^{36} - 6 q^{37} - 16 q^{38} + 10 q^{39} + 42 q^{40} - 8 q^{41} - 10 q^{43} - 30 q^{44} - 14 q^{45} - 10 q^{46} - 6 q^{47} - 40 q^{48} + 195 q^{49} - 2 q^{50} - 16 q^{51} + 16 q^{52} - 8 q^{53} - 22 q^{54} - 10 q^{55} - 28 q^{56} - 14 q^{57} + 8 q^{58} - 24 q^{59} + 46 q^{60} - 6 q^{61} - 32 q^{62} - 60 q^{63} + 232 q^{64} + 24 q^{65} - 18 q^{66} + 2 q^{67} - 52 q^{68} - 20 q^{69} + 28 q^{70} - 2 q^{71} - 22 q^{72} - 24 q^{73} + 24 q^{74} - 12 q^{75} - 2 q^{76} - 52 q^{77} - 52 q^{78} - 32 q^{79} - 48 q^{80} + 199 q^{81} + 66 q^{82} - 22 q^{83} - 128 q^{84} + 30 q^{85} - 40 q^{86} + 18 q^{87} - 4 q^{88} - 10 q^{89} - 10 q^{90} - 16 q^{91} - 70 q^{92} - 8 q^{93} + 26 q^{94} + 2 q^{95} + 34 q^{96} - 6 q^{97} - 106 q^{98} + 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2683))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2683
2683.2.a.a 2683.a 1.a $107$ $21.424$ None \(-22\) \(-24\) \(-72\) \(-14\) $+$ $\mathrm{SU}(2)$
2683.2.a.b 2683.a 1.a $116$ $21.424$ None \(20\) \(22\) \(72\) \(10\) $-$ $\mathrm{SU}(2)$