Properties

Label 8041.2.a
Level $8041$
Weight $2$
Character orbit 8041.a
Rep. character $\chi_{8041}(1,\cdot)$
Character field $\Q$
Dimension $559$
Newform subspaces $10$
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: \(\Q\)
Newform subspaces: \( 10 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\) into newform subspaces

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))
$5$ (\( 1 - 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 - 3 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))
$11$ (\( 1 - T \))(\( 1 + T \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))
$17$ (\( 1 - T \))(\( 1 - T \))
$19$ (\( 1 + 8 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))
$29$ (\( 1 + 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))
$41$ (\( 1 - 11 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))
$43$ (\( 1 + T \))(\( 1 + T \))
$47$ (\( 1 + 5 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))
$53$ (\( 1 - T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))
$59$ (\( 1 + 3 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))
$67$ (\( 1 + 9 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))
$71$ (\( 1 - 2 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))
$79$ (\( 1 - 4 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))
$89$ (\( 1 - 11 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))
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