Properties

Label 8041.2.a
Level 8041
Weight 2
Character orbit a
Rep. character \(\chi_{8041}(1,\cdot)\)
Character field \(\Q\)
Dimension 559
Newforms 10
Sturm bound 1584
Trace bound 2

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Defining parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)
Character field: \(\Q\)
Newforms: \( 10 \)
Sturm bound: \(1584\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8041))\).

Total New Old
Modular forms 796 559 237
Cusp forms 789 559 230
Eisenstein series 7 0 7

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

\(11\)\(17\)\(43\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(74\)
\(+\)\(+\)\(-\)\(-\)\(66\)
\(+\)\(-\)\(+\)\(-\)\(67\)
\(+\)\(-\)\(-\)\(+\)\(69\)
\(-\)\(+\)\(+\)\(-\)\(78\)
\(-\)\(+\)\(-\)\(+\)\(62\)
\(-\)\(-\)\(+\)\(+\)\(61\)
\(-\)\(-\)\(-\)\(-\)\(82\)
Plus space\(+\)\(266\)
Minus space\(-\)\(293\)

Trace form

\(559q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 553q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 551q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(559q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 553q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 551q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 529q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 541q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 36q^{27} \) \(\mathstrut -\mathstrut 32q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 40q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 33q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 549q^{36} \) \(\mathstrut -\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 56q^{42} \) \(\mathstrut -\mathstrut q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 22q^{45} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 28q^{48} \) \(\mathstrut +\mathstrut 507q^{49} \) \(\mathstrut -\mathstrut 37q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 26q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 48q^{54} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 38q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 32q^{60} \) \(\mathstrut -\mathstrut 62q^{61} \) \(\mathstrut -\mathstrut 56q^{62} \) \(\mathstrut -\mathstrut 72q^{63} \) \(\mathstrut +\mathstrut 577q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 28q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 7q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 52q^{71} \) \(\mathstrut +\mathstrut 141q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 98q^{74} \) \(\mathstrut -\mathstrut 84q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 144q^{78} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 567q^{81} \) \(\mathstrut +\mathstrut 98q^{82} \) \(\mathstrut -\mathstrut 68q^{83} \) \(\mathstrut -\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 3q^{86} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 33q^{88} \) \(\mathstrut -\mathstrut 66q^{89} \) \(\mathstrut +\mathstrut 38q^{90} \) \(\mathstrut -\mathstrut 112q^{91} \) \(\mathstrut +\mathstrut 104q^{92} \) \(\mathstrut +\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 132q^{96} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 109q^{98} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 17 43
8041.2.a.a \(1\) \(64.208\) \(\Q\) None \(-2\) \(-2\) \(2\) \(3\) \(-\) \(-\) \(+\) \(q-2q^{2}-2q^{3}+2q^{4}+2q^{5}+4q^{6}+\cdots\)
8041.2.a.b \(1\) \(64.208\) \(\Q\) None \(-1\) \(3\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}-q^{4}-2q^{5}-3q^{6}-2q^{7}+\cdots\)
8041.2.a.c \(60\) \(64.208\) None \(-9\) \(-6\) \(-15\) \(-17\) \(-\) \(-\) \(+\)
8041.2.a.d \(62\) \(64.208\) None \(-7\) \(-8\) \(-13\) \(-11\) \(-\) \(+\) \(-\)
8041.2.a.e \(66\) \(64.208\) None \(7\) \(3\) \(4\) \(14\) \(+\) \(+\) \(-\)
8041.2.a.f \(66\) \(64.208\) None \(12\) \(0\) \(6\) \(13\) \(+\) \(-\) \(+\)
8041.2.a.g \(69\) \(64.208\) None \(-11\) \(-3\) \(-6\) \(-11\) \(+\) \(-\) \(-\)
8041.2.a.h \(74\) \(64.208\) None \(-7\) \(-3\) \(-6\) \(-16\) \(+\) \(+\) \(+\)
8041.2.a.i \(78\) \(64.208\) None \(7\) \(10\) \(17\) \(11\) \(-\) \(+\) \(+\)
8041.2.a.j \(82\) \(64.208\) None \(8\) \(6\) \(11\) \(8\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(731))\)\(^{\oplus 2}\)