Properties

Label 4003.2
Level 4003
Weight 2
Dimension 665667
Nonzero newspaces 8
Sturm bound 2670668

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Defining parameters

Level: \( N \) = \( 4003\( 4003 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(2670668\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4003))\).

Total New Old
Modular forms 669668 669668 0
Cusp forms 665667 665667 0
Eisenstein series 4001 4001 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4003))\)

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
4003.2.a \(\chi_{4003}(1, \cdot)\) 4003.2.a.a 2 1
4003.2.a.b 152
4003.2.a.c 179
4003.2.c \(\chi_{4003}(822, \cdot)\) n/a 666 2
4003.2.e \(\chi_{4003}(551, \cdot)\) n/a 7304 22
4003.2.f \(\chi_{4003}(102, \cdot)\) n/a 9296 28
4003.2.i \(\chi_{4003}(129, \cdot)\) n/a 14652 44
4003.2.j \(\chi_{4003}(10, \cdot)\) n/a 18648 56
4003.2.m \(\chi_{4003}(6, \cdot)\) n/a 204512 616
4003.2.o \(\chi_{4003}(4, \cdot)\) n/a 410256 1232

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} + 4 T^{4} \))
$3$ (\( 1 + 4 T^{2} + 9 T^{4} \))
$5$ (\( 1 + 8 T^{2} + 25 T^{4} \))
$7$ (\( ( 1 + T + 7 T^{2} )^{2} \))
$11$ (\( 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} \))
$13$ (\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 2 T + 3 T^{2} + 34 T^{3} + 289 T^{4} \))
$19$ (\( 1 - 2 T + 7 T^{2} - 38 T^{3} + 361 T^{4} \))
$23$ (\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))
$29$ (\( 1 + 8 T + 66 T^{2} + 232 T^{3} + 841 T^{4} \))
$31$ (\( 1 - 4 T - 6 T^{2} - 124 T^{3} + 961 T^{4} \))
$37$ (\( 1 + 14 T + 115 T^{2} + 518 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 16 T + 138 T^{2} - 656 T^{3} + 1681 T^{4} \))
$43$ (\( ( 1 + 43 T^{2} )^{2} \))
$47$ (\( 1 - 8 T + 60 T^{2} - 376 T^{3} + 2209 T^{4} \))
$53$ (\( 1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 12 T + 146 T^{2} + 708 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 20 T + 214 T^{2} - 1220 T^{3} + 3721 T^{4} \))
$67$ (\( 1 - 14 T + 151 T^{2} - 938 T^{3} + 4489 T^{4} \))
$71$ (\( ( 1 - 6 T + 71 T^{2} )^{2} \))
$73$ (\( ( 1 + 3 T + 73 T^{2} )^{2} \))
$79$ (\( 1 - 6 T + 95 T^{2} - 474 T^{3} + 6241 T^{4} \))
$83$ (\( 1 - 6 T - 25 T^{2} - 498 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 18 T + 251 T^{2} + 1602 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 12 T + 212 T^{2} - 1164 T^{3} + 9409 T^{4} \))
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