Properties

Label 8049.2.a
Level 8049
Weight 2
Character orbit a
Rep. character \(\chi_{8049}(1,\cdot)\)
Character field \(\Q\)
Dimension 447
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8049))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 2683
8049.2.a.a \(95\) \(64.272\) None \(-9\) \(95\) \(-15\) \(-36\) \(-\) \(-\)
8049.2.a.b \(104\) \(64.272\) None \(-9\) \(-104\) \(-15\) \(-10\) \(+\) \(+\)
8049.2.a.c \(119\) \(64.272\) None \(11\) \(-119\) \(17\) \(10\) \(+\) \(-\)
8049.2.a.d \(129\) \(64.272\) None \(8\) \(129\) \(11\) \(40\) \(-\) \(+\)

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

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