# Properties

 Label 4024.2 Level 4024 Weight 2 Dimension 283630 Nonzero newspaces 6 Sturm bound 2.02406e+06

## 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

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