Properties

Label 8047.2.a
Level 8047
Weight 2
Character orbit a
Rep. character \(\chi_{8047}(1,\cdot)\)
Character field \(\Q\)
Dimension 619
Newforms 5
Sturm bound 1446
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1446\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8047))\).

Total New Old
Modular forms 724 619 105
Cusp forms 721 619 102
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.

\(13\)\(619\)FrickeDim.
\(+\)\(+\)\(+\)\(151\)
\(+\)\(-\)\(-\)\(158\)
\(-\)\(+\)\(-\)\(168\)
\(-\)\(-\)\(+\)\(142\)
Plus space\(+\)\(293\)
Minus space\(-\)\(326\)

Trace form

\(619q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 621q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 623q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(619q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 621q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 623q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 613q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 625q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut +\mathstrut 28q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 16q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 11q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 645q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 52q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 36q^{42} \) \(\mathstrut -\mathstrut 36q^{44} \) \(\mathstrut +\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 587q^{49} \) \(\mathstrut -\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut 52q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 56q^{60} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 76q^{62} \) \(\mathstrut +\mathstrut 32q^{63} \) \(\mathstrut +\mathstrut 573q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 58q^{68} \) \(\mathstrut +\mathstrut 20q^{69} \) \(\mathstrut -\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 85q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 62q^{80} \) \(\mathstrut +\mathstrut 643q^{81} \) \(\mathstrut -\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 52q^{84} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 8q^{88} \) \(\mathstrut -\mathstrut 38q^{89} \) \(\mathstrut -\mathstrut 186q^{90} \) \(\mathstrut -\mathstrut 32q^{92} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 32q^{96} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8047))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 619
8047.2.a.a \(2\) \(64.256\) \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(2\) \(-3\) \(+\) \(-\) \(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
8047.2.a.b \(142\) \(64.256\) None \(-13\) \(-26\) \(-37\) \(-14\) \(-\) \(-\)
8047.2.a.c \(151\) \(64.256\) None \(-13\) \(-16\) \(-43\) \(-18\) \(+\) \(+\)
8047.2.a.d \(156\) \(64.256\) None \(13\) \(23\) \(39\) \(19\) \(+\) \(-\)
8047.2.a.e \(168\) \(64.256\) None \(11\) \(26\) \(41\) \(12\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8047))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8047)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\)\(^{\oplus 2}\)