Properties

Label 4024.2
Level 4024
Weight 2
Dimension 283630
Nonzero newspaces 6
Sturm bound 2024064

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Defining parameters

Level: \( N \) = \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(2024064\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4024))\).

Total New Old
Modular forms 509028 285634 223394
Cusp forms 503005 283630 219375
Eisenstein series 6023 2004 4019

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4024))\)

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
4024.2.a \(\chi_{4024}(1, \cdot)\) 4024.2.a.a 1 1
4024.2.a.b 1
4024.2.a.c 1
4024.2.a.d 28
4024.2.a.e 29
4024.2.a.f 33
4024.2.a.g 33
4024.2.b \(\chi_{4024}(4023, \cdot)\) None 0 1
4024.2.c \(\chi_{4024}(2013, \cdot)\) n/a 502 1
4024.2.h \(\chi_{4024}(2011, \cdot)\) n/a 502 1
4024.2.i \(\chi_{4024}(9, \cdot)\) n/a 31500 250
4024.2.j \(\chi_{4024}(19, \cdot)\) n/a 125500 250
4024.2.o \(\chi_{4024}(13, \cdot)\) n/a 125500 250
4024.2.p \(\chi_{4024}(15, \cdot)\) None 0 250

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))(\( \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))
$23$ (\( 1 + 9 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))
$43$ (\( 1 + 5 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))
$47$ (\( 1 - T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))
$59$ (\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))
$61$ (\( 1 + 3 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))
$67$ (\( 1 + 5 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))
$71$ (\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))
$83$ (\( 1 - 7 T + 83 T^{2} \))(\( 1 + 17 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))
$97$ (\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))
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