Properties

Label 8045.2.a
Level 8045
Weight 2
Character orbit a
Rep. character \(\chi_{8045}(1,\cdot)\)
Character field \(\Q\)
Dimension 537
Newforms 5
Sturm bound 1610
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8045 = 5 \cdot 1609 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8045.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1610\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8045))\).

Total New Old
Modular forms 806 537 269
Cusp forms 803 537 266
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.

\(5\)\(1609\)FrickeDim.
\(+\)\(+\)\(+\)\(126\)
\(+\)\(-\)\(-\)\(142\)
\(-\)\(+\)\(-\)\(142\)
\(-\)\(-\)\(+\)\(127\)
Plus space\(+\)\(253\)
Minus space\(-\)\(284\)

Trace form

\(537q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 539q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 545q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(537q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 539q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 545q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 539q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 29q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 537q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 29q^{32} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 563q^{36} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut -\mathstrut 40q^{42} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 52q^{44} \) \(\mathstrut +\mathstrut 13q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 28q^{48} \) \(\mathstrut +\mathstrut 581q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 72q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut -\mathstrut 66q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 72q^{62} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 495q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 113q^{72} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 62q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 593q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 60q^{84} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 48q^{87} \) \(\mathstrut -\mathstrut 60q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 39q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 88q^{92} \) \(\mathstrut -\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 80q^{96} \) \(\mathstrut +\mathstrut 46q^{97} \) \(\mathstrut -\mathstrut 69q^{98} \) \(\mathstrut -\mathstrut 72q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8045))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 1609
8045.2.a.a \(1\) \(64.240\) \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\)
8045.2.a.b \(126\) \(64.240\) None \(5\) \(-9\) \(-126\) \(-23\) \(+\) \(+\)
8045.2.a.c \(127\) \(64.240\) None \(-20\) \(-31\) \(127\) \(-63\) \(-\) \(-\)
8045.2.a.d \(141\) \(64.240\) None \(-8\) \(11\) \(-141\) \(29\) \(+\) \(-\)
8045.2.a.e \(142\) \(64.240\) None \(21\) \(33\) \(142\) \(63\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8045))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1609))\)\(^{\oplus 2}\)