# Properties

 Label 4015.2 Level 4015 Weight 2 Dimension 572267 Nonzero newspaces 84 Sturm bound 2.55744e+06

## Defining parameters

 Level: $$N$$ = $$4015 = 5 \cdot 11 \cdot 73$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$2557440$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4015))$$.

Total New Old
Modular forms 645120 579931 65189
Cusp forms 633601 572267 61334
Eisenstein series 11519 7664 3855

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4015))$$

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
4015.2.a $$\chi_{4015}(1, \cdot)$$ 4015.2.a.a 1 1
4015.2.a.b 23
4015.2.a.c 23
4015.2.a.d 27
4015.2.a.e 27
4015.2.a.f 31
4015.2.a.g 32
4015.2.a.h 37
4015.2.a.i 38
4015.2.b $$\chi_{4015}(804, \cdot)$$ n/a 360 1
4015.2.c $$\chi_{4015}(364, \cdot)$$ n/a 368 1
4015.2.h $$\chi_{4015}(3576, \cdot)$$ n/a 244 1
4015.2.i $$\chi_{4015}(1541, \cdot)$$ n/a 488 2
4015.2.k $$\chi_{4015}(2509, \cdot)$$ n/a 744 2
4015.2.m $$\chi_{4015}(1242, \cdot)$$ n/a 864 2
4015.2.n $$\chi_{4015}(802, \cdot)$$ n/a 880 2
4015.2.p $$\chi_{4015}(538, \cdot)$$ n/a 880 2
4015.2.s $$\chi_{4015}(703, \cdot)$$ n/a 880 2
4015.2.t $$\chi_{4015}(1706, \cdot)$$ n/a 488 2
4015.2.v $$\chi_{4015}(366, \cdot)$$ n/a 1152 4
4015.2.y $$\chi_{4015}(1761, \cdot)$$ n/a 488 2
4015.2.z $$\chi_{4015}(2344, \cdot)$$ n/a 736 2
4015.2.ba $$\chi_{4015}(2564, \cdot)$$ n/a 736 2
4015.2.be $$\chi_{4015}(241, \cdot)$$ n/a 1184 4
4015.2.bf $$\chi_{4015}(2168, \cdot)$$ n/a 1480 4
4015.2.bh $$\chi_{4015}(562, \cdot)$$ n/a 1480 4
4015.2.bj $$\chi_{4015}(1044, \cdot)$$ n/a 1760 4
4015.2.bl $$\chi_{4015}(221, \cdot)$$ n/a 1488 6
4015.2.bm $$\chi_{4015}(291, \cdot)$$ n/a 1184 4
4015.2.br $$\chi_{4015}(729, \cdot)$$ n/a 1760 4
4015.2.bs $$\chi_{4015}(1169, \cdot)$$ n/a 1728 4
4015.2.bt $$\chi_{4015}(441, \cdot)$$ n/a 976 4
4015.2.bv $$\chi_{4015}(1363, \cdot)$$ n/a 1760 4
4015.2.by $$\chi_{4015}(362, \cdot)$$ n/a 1760 4
4015.2.ca $$\chi_{4015}(593, \cdot)$$ n/a 1760 4
4015.2.cb $$\chi_{4015}(373, \cdot)$$ n/a 1760 4
4015.2.ce $$\chi_{4015}(1244, \cdot)$$ n/a 1488 4
4015.2.cf $$\chi_{4015}(81, \cdot)$$ n/a 2368 8
4015.2.ch $$\chi_{4015}(276, \cdot)$$ n/a 1488 6
4015.2.ck $$\chi_{4015}(144, \cdot)$$ n/a 2208 6
4015.2.cm $$\chi_{4015}(89, \cdot)$$ n/a 2208 6
4015.2.co $$\chi_{4015}(246, \cdot)$$ n/a 2368 8
4015.2.cp $$\chi_{4015}(338, \cdot)$$ n/a 3520 8
4015.2.cs $$\chi_{4015}(173, \cdot)$$ n/a 3520 8
4015.2.cu $$\chi_{4015}(72, \cdot)$$ n/a 3520 8
4015.2.cv $$\chi_{4015}(293, \cdot)$$ n/a 3456 8
4015.2.cx $$\chi_{4015}(119, \cdot)$$ n/a 3520 8
4015.2.da $$\chi_{4015}(494, \cdot)$$ n/a 3520 8
4015.2.dc $$\chi_{4015}(408, \cdot)$$ n/a 2960 8
4015.2.de $$\chi_{4015}(518, \cdot)$$ n/a 2960 8
4015.2.df $$\chi_{4015}(21, \cdot)$$ n/a 2368 8
4015.2.dj $$\chi_{4015}(9, \cdot)$$ n/a 3520 8
4015.2.dk $$\chi_{4015}(64, \cdot)$$ n/a 3520 8
4015.2.dl $$\chi_{4015}(301, \cdot)$$ n/a 2368 8
4015.2.dp $$\chi_{4015}(254, \cdot)$$ n/a 4464 12
4015.2.dr $$\chi_{4015}(692, \cdot)$$ n/a 5280 12
4015.2.ds $$\chi_{4015}(142, \cdot)$$ n/a 5280 12
4015.2.du $$\chi_{4015}(32, \cdot)$$ n/a 5280 12
4015.2.dx $$\chi_{4015}(98, \cdot)$$ n/a 5280 12
4015.2.dy $$\chi_{4015}(111, \cdot)$$ n/a 2976 12
4015.2.eb $$\chi_{4015}(314, \cdot)$$ n/a 7040 16
4015.2.ed $$\chi_{4015}(752, \cdot)$$ n/a 7040 16
4015.2.ef $$\chi_{4015}(168, \cdot)$$ n/a 7040 16
4015.2.eg $$\chi_{4015}(51, \cdot)$$ n/a 4736 16
4015.2.ei $$\chi_{4015}(16, \cdot)$$ n/a 7104 24
4015.2.ej $$\chi_{4015}(49, \cdot)$$ n/a 7040 16
4015.2.em $$\chi_{4015}(8, \cdot)$$ n/a 7040 16
4015.2.en $$\chi_{4015}(138, \cdot)$$ n/a 7040 16
4015.2.ep $$\chi_{4015}(733, \cdot)$$ n/a 7040 16
4015.2.es $$\chi_{4015}(222, \cdot)$$ n/a 7040 16
4015.2.eu $$\chi_{4015}(581, \cdot)$$ n/a 4736 16
4015.2.ev $$\chi_{4015}(78, \cdot)$$ n/a 8880 24
4015.2.ex $$\chi_{4015}(604, \cdot)$$ n/a 10560 24
4015.2.ez $$\chi_{4015}(131, \cdot)$$ n/a 7104 24
4015.2.fb $$\chi_{4015}(133, \cdot)$$ n/a 8880 24
4015.2.fd $$\chi_{4015}(4, \cdot)$$ n/a 10560 24
4015.2.ff $$\chi_{4015}(69, \cdot)$$ n/a 10560 24
4015.2.fi $$\chi_{4015}(36, \cdot)$$ n/a 7104 24
4015.2.fl $$\chi_{4015}(116, \cdot)$$ n/a 9472 32
4015.2.fm $$\chi_{4015}(163, \cdot)$$ n/a 14080 32
4015.2.fo $$\chi_{4015}(103, \cdot)$$ n/a 14080 32
4015.2.fq $$\chi_{4015}(94, \cdot)$$ n/a 14080 32
4015.2.ft $$\chi_{4015}(181, \cdot)$$ n/a 14208 48
4015.2.fu $$\chi_{4015}(123, \cdot)$$ n/a 21120 48
4015.2.fx $$\chi_{4015}(18, \cdot)$$ n/a 21120 48
4015.2.fz $$\chi_{4015}(2, \cdot)$$ n/a 21120 48
4015.2.ga $$\chi_{4015}(127, \cdot)$$ n/a 21120 48
4015.2.gc $$\chi_{4015}(169, \cdot)$$ n/a 21120 48
4015.2.gf $$\chi_{4015}(58, \cdot)$$ n/a 42240 96
4015.2.gh $$\chi_{4015}(101, \cdot)$$ n/a 28416 96
4015.2.gj $$\chi_{4015}(29, \cdot)$$ n/a 42240 96
4015.2.gl $$\chi_{4015}(42, \cdot)$$ n/a 42240 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4015))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4015)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(73))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(365))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(803))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

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