Properties

Label 8049.2.a
Level $8049$
Weight $2$
Character orbit 8049.a
Rep. character $\chi_{8049}(1,\cdot)$
Character field $\Q$
Dimension $447$
Newform subspaces $4$
Sturm bound $1789$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8049 = 3 \cdot 2683 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8049.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1789\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8049))\).

Total New Old
Modular forms 896 447 449
Cusp forms 893 447 446
Eisenstein series 3 0 3

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

\(3\)\(2683\)FrickeDim
\(+\)\(+\)$+$\(104\)
\(+\)\(-\)$-$\(119\)
\(-\)\(+\)$-$\(129\)
\(-\)\(-\)$+$\(95\)
Plus space\(+\)\(199\)
Minus space\(-\)\(248\)

Trace form

\( 447 q + q^{2} + q^{3} + 447 q^{4} - 2 q^{5} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 447 q^{9} + O(q^{10}) \) \( 447 q + q^{2} + q^{3} + 447 q^{4} - 2 q^{5} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 447 q^{9} - 18 q^{10} + 4 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} - 6 q^{15} + 451 q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + 10 q^{20} + 4 q^{21} + 4 q^{22} + 12 q^{23} - 15 q^{24} + 425 q^{25} + 2 q^{26} + q^{27} - 16 q^{28} + 2 q^{29} - 14 q^{30} + 8 q^{31} + 5 q^{32} - 4 q^{33} - 2 q^{34} - 8 q^{35} + 447 q^{36} + 18 q^{37} + 12 q^{38} + 6 q^{39} - 42 q^{40} - 10 q^{41} - 12 q^{42} - 4 q^{43} + 60 q^{44} - 2 q^{45} + 8 q^{46} + 16 q^{47} - q^{48} + 459 q^{49} - q^{50} + 2 q^{51} - 14 q^{52} + 18 q^{53} - 3 q^{54} + 28 q^{55} + 16 q^{56} + 8 q^{57} + 14 q^{58} + 16 q^{59} - 42 q^{60} - 2 q^{61} + 4 q^{62} + 4 q^{63} + 443 q^{64} - 60 q^{65} + 12 q^{66} - 24 q^{67} + 30 q^{68} - 36 q^{70} + 28 q^{71} - 3 q^{72} + 6 q^{73} - 2 q^{74} - q^{75} - 4 q^{76} + 40 q^{77} - 14 q^{78} + 48 q^{79} + 38 q^{80} + 447 q^{81} - 46 q^{82} + 28 q^{83} + 4 q^{84} - 24 q^{85} + 60 q^{86} - 18 q^{87} + 28 q^{88} - 30 q^{89} - 18 q^{90} + 28 q^{91} + 60 q^{92} - 8 q^{94} - 4 q^{95} - 63 q^{96} + 2 q^{97} + 41 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8049))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 2683
8049.2.a.a 8049.a 1.a $95$ $64.272$ None \(-9\) \(95\) \(-15\) \(-36\) $-$ $-$ $\mathrm{SU}(2)$
8049.2.a.b 8049.a 1.a $104$ $64.272$ None \(-9\) \(-104\) \(-15\) \(-10\) $+$ $+$ $\mathrm{SU}(2)$
8049.2.a.c 8049.a 1.a $119$ $64.272$ None \(11\) \(-119\) \(17\) \(10\) $+$ $-$ $\mathrm{SU}(2)$
8049.2.a.d 8049.a 1.a $129$ $64.272$ None \(8\) \(129\) \(11\) \(40\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8049))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8049)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2683))\)\(^{\oplus 2}\)