# Properties

 Label 6041.2 Level 6041 Weight 2 Dimension 1.42316e+06 Nonzero newspaces 8 Sturm bound 5.95814e+06

## Defining parameters

 Level: $$N$$ = $$6041 = 7 \cdot 863$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$5958144$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6041))$$.

Total New Old
Modular forms 1494708 1431773 62935
Cusp forms 1484365 1423161 61204
Eisenstein series 10343 8612 1731

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6041))$$

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
6041.2.a $$\chi_{6041}(1, \cdot)$$ 6041.2.a.a 1 1
6041.2.a.b 2
6041.2.a.c 83
6041.2.a.d 101
6041.2.a.e 112
6041.2.a.f 132
6041.2.c $$\chi_{6041}(6040, \cdot)$$ n/a 574 1
6041.2.e $$\chi_{6041}(3453, \cdot)$$ n/a 1148 2
6041.2.g $$\chi_{6041}(1725, \cdot)$$ n/a 1148 2
6041.2.i $$\chi_{6041}(8, \cdot)$$ n/a 185760 430
6041.2.k $$\chi_{6041}(13, \cdot)$$ n/a 246820 430
6041.2.m $$\chi_{6041}(2, \cdot)$$ n/a 493640 860
6041.2.o $$\chi_{6041}(5, \cdot)$$ n/a 493640 860

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6041))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6041)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(863))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - T + 2 T^{2}$$)($$( 1 + T + 2 T^{2} )^{2}$$)
$3$ ($$1 - 2 T + 3 T^{2}$$)($$1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4}$$)
$5$ ($$1 + 4 T + 5 T^{2}$$)($$1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4}$$)
$7$ ($$1 - T$$)($$( 1 + T )^{2}$$)
$11$ ($$1 + 4 T + 11 T^{2}$$)($$1 + 3 T + 23 T^{2} + 33 T^{3} + 121 T^{4}$$)
$13$ ($$1 + 4 T + 13 T^{2}$$)($$1 - 9 T + 45 T^{2} - 117 T^{3} + 169 T^{4}$$)
$17$ ($$1 + 6 T + 17 T^{2}$$)($$1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4}$$)
$19$ ($$1 - 6 T + 19 T^{2}$$)($$1 - 3 T + 9 T^{2} - 57 T^{3} + 361 T^{4}$$)
$23$ ($$1 + 8 T + 23 T^{2}$$)($$1 + T + 15 T^{2} + 23 T^{3} + 529 T^{4}$$)
$29$ ($$1 - 6 T + 29 T^{2}$$)($$1 + 38 T^{2} + 841 T^{4}$$)
$31$ ($$1 - 2 T + 31 T^{2}$$)($$1 + 4 T + 46 T^{2} + 124 T^{3} + 961 T^{4}$$)
$37$ ($$1 - 10 T + 37 T^{2}$$)($$1 + 11 T + 93 T^{2} + 407 T^{3} + 1369 T^{4}$$)
$41$ ($$1 - 6 T + 41 T^{2}$$)($$1 + 2 T^{2} + 1681 T^{4}$$)
$43$ ($$1 + 4 T + 43 T^{2}$$)($$1 - 2 T + 42 T^{2} - 86 T^{3} + 1849 T^{4}$$)
$47$ ($$1 + 47 T^{2}$$)($$1 + 2 T + 90 T^{2} + 94 T^{3} + 2209 T^{4}$$)
$53$ ($$1 - 2 T + 53 T^{2}$$)($$1 - 7 T + 57 T^{2} - 371 T^{3} + 2809 T^{4}$$)
$59$ ($$1 - 10 T + 59 T^{2}$$)($$1 + 19 T + 207 T^{2} + 1121 T^{3} + 3481 T^{4}$$)
$61$ ($$1 + 10 T + 61 T^{2}$$)($$1 - 14 T + 126 T^{2} - 854 T^{3} + 3721 T^{4}$$)
$67$ ($$1 + 4 T + 67 T^{2}$$)($$1 + 21 T + 233 T^{2} + 1407 T^{3} + 4489 T^{4}$$)
$71$ ($$1 - 8 T + 71 T^{2}$$)($$1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4}$$)
$73$ ($$1 - 4 T + 73 T^{2}$$)($$1 - 3 T + 137 T^{2} - 219 T^{3} + 5329 T^{4}$$)
$79$ ($$1 + 79 T^{2}$$)($$1 + 25 T + 313 T^{2} + 1975 T^{3} + 6241 T^{4}$$)
$83$ ($$1 + 4 T + 83 T^{2}$$)($$1 - 22 T + 282 T^{2} - 1826 T^{3} + 6889 T^{4}$$)
$89$ ($$1 - 4 T + 89 T^{2}$$)($$1 - 4 T + 102 T^{2} - 356 T^{3} + 7921 T^{4}$$)
$97$ ($$1 + 8 T + 97 T^{2}$$)($$1 + 3 T + 185 T^{2} + 291 T^{3} + 9409 T^{4}$$)