# Properties

 Label 4027.2 Level 4027 Weight 2 Dimension 673685 Nonzero newspaces 8 Sturm bound 2.70279e+06

## 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

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