Properties

Label 6041.2
Level 6041
Weight 2
Dimension 1423161
Nonzero newspaces 8
Sturm bound 5958144

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Defining parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(5958144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6041))\).

Total New Old
Modular forms 1494708 1431773 62935
Cusp forms 1484365 1423161 61204
Eisenstein series 10343 8612 1731

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6041))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6041.2.a \(\chi_{6041}(1, \cdot)\) 6041.2.a.a 1 1
6041.2.a.b 2
6041.2.a.c 83
6041.2.a.d 101
6041.2.a.e 112
6041.2.a.f 132
6041.2.c \(\chi_{6041}(6040, \cdot)\) n/a 574 1
6041.2.e \(\chi_{6041}(3453, \cdot)\) n/a 1148 2
6041.2.g \(\chi_{6041}(1725, \cdot)\) n/a 1148 2
6041.2.i \(\chi_{6041}(8, \cdot)\) n/a 185760 430
6041.2.k \(\chi_{6041}(13, \cdot)\) n/a 246820 430
6041.2.m \(\chi_{6041}(2, \cdot)\) n/a 493640 860
6041.2.o \(\chi_{6041}(5, \cdot)\) n/a 493640 860

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6041))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(863))\)\(^{\oplus 2}\)

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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