Properties

Label 6038.2
Level 6038
Weight 2
Dimension 379764
Nonzero newspaces 4
Sturm bound 4557180

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Defining parameters

Level: \( N \) = \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4557180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6038))\).

Total New Old
Modular forms 1142313 379764 762549
Cusp forms 1136278 379764 756514
Eisenstein series 6035 0 6035

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6038))\)

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
6038.2.a \(\chi_{6038}(1, \cdot)\) 6038.2.a.a 2 1
6038.2.a.b 54
6038.2.a.c 57
6038.2.a.d 69
6038.2.a.e 70
6038.2.c \(\chi_{6038}(239, \cdot)\) n/a 502 2
6038.2.e \(\chi_{6038}(9, \cdot)\) n/a 127006 502
6038.2.g \(\chi_{6038}(5, \cdot)\) n/a 252004 1004

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(3019))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T )^{2} \))
$3$ (\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))
$5$ (\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))
$7$ (\( ( 1 + 3 T + 7 T^{2} )^{2} \))
$11$ (\( 1 + 7 T + 33 T^{2} + 77 T^{3} + 121 T^{4} \))
$13$ (\( ( 1 + 3 T + 13 T^{2} )^{2} \))
$17$ (\( 1 + 6 T + 23 T^{2} + 102 T^{3} + 289 T^{4} \))
$19$ (\( ( 1 + 3 T + 19 T^{2} )^{2} \))
$23$ (\( 1 + 6 T + 35 T^{2} + 138 T^{3} + 529 T^{4} \))
$29$ (\( 1 + 14 T + 102 T^{2} + 406 T^{3} + 841 T^{4} \))
$31$ (\( 1 + T + 31 T^{2} + 31 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 3 T + 65 T^{2} - 111 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 43 T^{2} + 1681 T^{4} \))
$43$ (\( 1 + 14 T + 130 T^{2} + 602 T^{3} + 1849 T^{4} \))
$47$ (\( 1 - 3 T - 5 T^{2} - 141 T^{3} + 2209 T^{4} \))
$53$ (\( ( 1 + 9 T + 53 T^{2} )^{2} \))
$59$ (\( 1 + 24 T + 257 T^{2} + 1416 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 7 T + 133 T^{2} + 427 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 3 T + 125 T^{2} + 201 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 6 T + 71 T^{2} + 426 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 12 T + 137 T^{2} + 876 T^{3} + 5329 T^{4} \))
$79$ (\( 1 - 3 T + 149 T^{2} - 237 T^{3} + 6241 T^{4} \))
$83$ (\( 1 - 14 T + 135 T^{2} - 1162 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 9 T + 47 T^{2} + 801 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 32 T + 445 T^{2} - 3104 T^{3} + 9409 T^{4} \))
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