Properties

Label 4027.2
Level 4027
Weight 2
Dimension 673685
Nonzero newspaces 8
Sturm bound 2702788

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Defining parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(2702788\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4027))\).

Total New Old
Modular forms 677710 677710 0
Cusp forms 673685 673685 0
Eisenstein series 4025 4025 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4027))\)

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
4027.2.a \(\chi_{4027}(1, \cdot)\) 4027.2.a.a 2 1
4027.2.a.b 159
4027.2.a.c 174
4027.2.c \(\chi_{4027}(1820, \cdot)\) n/a 670 2
4027.2.e \(\chi_{4027}(14, \cdot)\) n/a 3340 10
4027.2.g \(\chi_{4027}(130, \cdot)\) n/a 6700 20
4027.2.h \(\chi_{4027}(13, \cdot)\) n/a 20040 60
4027.2.k \(\chi_{4027}(41, \cdot)\) n/a 40200 120
4027.2.m \(\chi_{4027}(4, \cdot)\) n/a 200400 600
4027.2.o \(\chi_{4027}(6, \cdot)\) n/a 402000 1200

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))
$3$ (\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))
$5$ (\( ( 1 + T + 5 T^{2} )^{2} \))
$7$ (\( 1 + 7 T + 25 T^{2} + 49 T^{3} + 49 T^{4} \))
$11$ (\( ( 1 + T + 11 T^{2} )^{2} \))
$13$ (\( 1 + 3 T + 27 T^{2} + 39 T^{3} + 169 T^{4} \))
$17$ (\( 1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4} \))
$19$ (\( ( 1 + 5 T + 19 T^{2} )^{2} \))
$23$ (\( 1 + 11 T + 75 T^{2} + 253 T^{3} + 529 T^{4} \))
$29$ (\( 1 + 9 T + 77 T^{2} + 261 T^{3} + 841 T^{4} \))
$31$ (\( 1 + 12 T + 93 T^{2} + 372 T^{3} + 961 T^{4} \))
$37$ (\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))
$41$ (\( 1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4} \))
$43$ (\( 1 - 4 T + 45 T^{2} - 172 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 8 T + 90 T^{2} + 376 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 8 T + 117 T^{2} - 424 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 4 T + 77 T^{2} + 236 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 3 T^{2} + 3721 T^{4} \))
$67$ (\( 1 - 2 T + 90 T^{2} - 134 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 15 T + 187 T^{2} + 1065 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 11 T + 145 T^{2} + 803 T^{3} + 5329 T^{4} \))
$79$ (\( ( 1 - 13 T + 79 T^{2} )^{2} \))
$83$ (\( 1 + 13 T + 107 T^{2} + 1079 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 15 T + 223 T^{2} + 1335 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 18 T + 255 T^{2} - 1746 T^{3} + 9409 T^{4} \))
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