# Properties

 Label 5077.2 Level 5077 Weight 2 Dimension 1.07146e+06 Nonzero newspaces 16 Sturm bound 4.29599e+06

## Defining parameters

 Level: $$N$$ = $$5077$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$4295988$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5077))$$.

Total New Old
Modular forms 1076535 1076535 0
Cusp forms 1071460 1071460 0
Eisenstein series 5075 5075 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5077))$$

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
5077.2.a $$\chi_{5077}(1, \cdot)$$ 5077.2.a.a 1 1
5077.2.a.b 205
5077.2.a.c 216
5077.2.b $$\chi_{5077}(5076, \cdot)$$ n/a 422 1
5077.2.c $$\chi_{5077}(1629, \cdot)$$ n/a 842 2
5077.2.e $$\chi_{5077}(1630, \cdot)$$ n/a 844 2
5077.2.f $$\chi_{5077}(360, \cdot)$$ n/a 2526 6
5077.2.h $$\chi_{5077}(2402, \cdot)$$ n/a 2532 6
5077.2.i $$\chi_{5077}(382, \cdot)$$ n/a 7596 18
5077.2.k $$\chi_{5077}(321, \cdot)$$ n/a 19366 46
5077.2.l $$\chi_{5077}(21, \cdot)$$ n/a 7614 18
5077.2.m $$\chi_{5077}(25, \cdot)$$ n/a 19412 46
5077.2.o $$\chi_{5077}(89, \cdot)$$ n/a 38732 92
5077.2.q $$\chi_{5077}(22, \cdot)$$ n/a 38824 92
5077.2.r $$\chi_{5077}(9, \cdot)$$ n/a 116196 276
5077.2.t $$\chi_{5077}(3, \cdot)$$ n/a 116472 276
5077.2.u $$\chi_{5077}(7, \cdot)$$ n/a 349416 828
5077.2.w $$\chi_{5077}(4, \cdot)$$ n/a 350244 828

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

## Hecke characteristic polynomials

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