Properties

Label 6041.2.a
Level $6041$
Weight $2$
Character orbit 6041.a
Rep. character $\chi_{6041}(1,\cdot)$
Character field $\Q$
Dimension $431$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6041))\).

Total New Old
Modular forms 578 431 147
Cusp forms 575 431 144
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.

\(7\)\(863\)FrickeDim.
\(+\)\(+\)\(+\)\(103\)
\(+\)\(-\)\(-\)\(112\)
\(-\)\(+\)\(-\)\(133\)
\(-\)\(-\)\(+\)\(83\)
Plus space\(+\)\(186\)
Minus space\(-\)\(245\)

Trace form

\( 431q - q^{2} + 435q^{4} - 2q^{5} + 8q^{6} + q^{7} + 3q^{8} + 423q^{9} + O(q^{10}) \) \( 431q - q^{2} + 435q^{4} - 2q^{5} + 8q^{6} + q^{7} + 3q^{8} + 423q^{9} + 6q^{10} + 16q^{12} - 14q^{13} + 3q^{14} + 12q^{15} + 455q^{16} - 14q^{17} - 9q^{18} - 6q^{20} + 24q^{22} + 16q^{23} + 20q^{24} + 421q^{25} + 30q^{26} + 12q^{27} + 7q^{28} - 18q^{29} + 20q^{30} + 20q^{31} + 15q^{32} - 44q^{33} + 2q^{34} - 6q^{35} + 463q^{36} - 6q^{37} - 52q^{38} + 24q^{39} + 26q^{40} - 26q^{41} + 12q^{42} - 8q^{44} + 14q^{45} + 32q^{46} + 16q^{47} - 16q^{48} + 431q^{49} - 15q^{50} - 4q^{51} - 46q^{52} + 14q^{53} - 20q^{54} + 32q^{55} + 15q^{56} - 4q^{57} - 26q^{58} - 44q^{60} - 14q^{61} - 24q^{62} + 13q^{63} + 519q^{64} - 20q^{65} - 28q^{66} + 12q^{67} - 34q^{68} + 20q^{69} - 10q^{70} + 8q^{71} + 19q^{72} - 34q^{73} - 14q^{74} + 40q^{76} + 4q^{77} - 12q^{78} + 32q^{79} - 2q^{80} + 391q^{81} + 62q^{82} - 16q^{83} + 12q^{84} + 4q^{85} + 52q^{86} - 32q^{87} + 68q^{88} - 6q^{89} - 138q^{90} - 6q^{91} + 60q^{92} + 48q^{93} + 92q^{94} + 40q^{95} + 92q^{96} - 26q^{97} - q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6041))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 863
6041.2.a.a \(1\) \(48.238\) \(\Q\) None \(1\) \(2\) \(-4\) \(1\) \(-\) \(+\) \(q+q^{2}+2q^{3}-q^{4}-4q^{5}+2q^{6}+q^{7}+\cdots\)
6041.2.a.b \(2\) \(48.238\) \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(1\) \(-2\) \(+\) \(+\) \(q-q^{2}+(1+\beta )q^{3}-q^{4}+(1-\beta )q^{5}+\cdots\)
6041.2.a.c \(83\) \(48.238\) None \(-8\) \(-12\) \(-11\) \(83\) \(-\) \(-\)
6041.2.a.d \(101\) \(48.238\) None \(3\) \(-17\) \(-12\) \(-101\) \(+\) \(+\)
6041.2.a.e \(112\) \(48.238\) None \(-3\) \(14\) \(13\) \(-112\) \(+\) \(-\)
6041.2.a.f \(132\) \(48.238\) None \(8\) \(10\) \(11\) \(132\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(863))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + 2 T^{2} \))(\( ( 1 + T + 2 T^{2} )^{2} \))
$3$ (\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))
$7$ (\( 1 - T \))(\( ( 1 + T )^{2} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 23 T^{2} + 33 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))(\( 1 - 9 T + 45 T^{2} - 117 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4} \))
$19$ (\( 1 - 6 T + 19 T^{2} \))(\( 1 - 3 T + 9 T^{2} - 57 T^{3} + 361 T^{4} \))
$23$ (\( 1 + 8 T + 23 T^{2} \))(\( 1 + T + 15 T^{2} + 23 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 + 38 T^{2} + 841 T^{4} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 + 4 T + 46 T^{2} + 124 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 10 T + 37 T^{2} \))(\( 1 + 11 T + 93 T^{2} + 407 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T^{2} + 1681 T^{4} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - 2 T + 42 T^{2} - 86 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 2 T + 90 T^{2} + 94 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 - 7 T + 57 T^{2} - 371 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))(\( 1 + 19 T + 207 T^{2} + 1121 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 14 T + 126 T^{2} - 854 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 + 21 T + 233 T^{2} + 1407 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))
$73$ (\( 1 - 4 T + 73 T^{2} \))(\( 1 - 3 T + 137 T^{2} - 219 T^{3} + 5329 T^{4} \))
$79$ (\( 1 + 79 T^{2} \))(\( 1 + 25 T + 313 T^{2} + 1975 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 22 T + 282 T^{2} - 1826 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 4 T + 89 T^{2} \))(\( 1 - 4 T + 102 T^{2} - 356 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 + 3 T + 185 T^{2} + 291 T^{3} + 9409 T^{4} \))
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