# Properties

 Label 1155.2.l Level 1155 Weight 2 Character orbit l Rep. character $$\chi_{1155}(1121,\cdot)$$ Character field $$\Q$$ Dimension 96 Newform subspaces 6 Sturm bound 384 Trace bound 11

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1155 = 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1155.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$384$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1155, [\chi])$$.

Total New Old
Modular forms 200 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

## Trace form

 $$96q + 8q^{3} + 96q^{4} - 20q^{9} + O(q^{10})$$ $$96q + 8q^{3} + 96q^{4} - 20q^{9} + 24q^{12} + 4q^{15} + 128q^{16} + 8q^{22} - 96q^{25} - 16q^{27} - 4q^{33} + 32q^{34} - 8q^{36} - 16q^{37} + 56q^{48} - 96q^{49} - 8q^{55} - 64q^{58} + 16q^{60} + 160q^{64} - 60q^{66} - 112q^{67} - 56q^{69} - 8q^{75} - 88q^{78} - 12q^{81} - 16q^{88} - 24q^{91} - 24q^{93} + 80q^{97} - 30q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1155, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1155.2.l.a $$4$$ $$9.223$$ $$\Q(\zeta_{8})$$ None $$-4$$ $$4$$ $$0$$ $$0$$ $$q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots$$
1155.2.l.b $$4$$ $$9.223$$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots$$
1155.2.l.c $$4$$ $$9.223$$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots$$
1155.2.l.d $$4$$ $$9.223$$ $$\Q(\zeta_{8})$$ None $$4$$ $$4$$ $$0$$ $$0$$ $$q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots$$
1155.2.l.e $$40$$ $$9.223$$ None $$-4$$ $$-4$$ $$0$$ $$0$$
1155.2.l.f $$40$$ $$9.223$$ None $$4$$ $$-4$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1155, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1155, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4} )^{2}$$)
$3$ ($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)
$5$ ($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)
$7$ ($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)
$11$ ($$1 + 14 T^{2} + 121 T^{4}$$)($$( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}$$)($$1 + 14 T^{2} + 121 T^{4}$$)
$13$ ($$( 1 - 13 T^{2} )^{4}$$)($$1 - 8 T^{2} + 66 T^{4} - 1352 T^{6} + 28561 T^{8}$$)($$1 - 8 T^{2} + 66 T^{4} - 1352 T^{6} + 28561 T^{8}$$)($$( 1 - 13 T^{2} )^{4}$$)
$17$ ($$( 1 - 8 T + 42 T^{2} - 136 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 6 T + 35 T^{2} + 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 6 T + 35 T^{2} - 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 8 T + 42 T^{2} + 136 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8}$$)($$1 - 38 T^{2} + 1011 T^{4} - 13718 T^{6} + 130321 T^{8}$$)($$1 - 38 T^{2} + 1011 T^{4} - 13718 T^{6} + 130321 T^{8}$$)($$1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8}$$)
$23$ ($$1 - 68 T^{2} + 2086 T^{4} - 35972 T^{6} + 279841 T^{8}$$)($$1 - 38 T^{2} + 771 T^{4} - 20102 T^{6} + 279841 T^{8}$$)($$1 - 38 T^{2} + 771 T^{4} - 20102 T^{6} + 279841 T^{8}$$)($$1 - 68 T^{2} + 2086 T^{4} - 35972 T^{6} + 279841 T^{8}$$)
$29$ ($$( 1 + 26 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 6 T + 59 T^{2} - 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 6 T + 59 T^{2} + 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 841 T^{4} )^{2}$$)
$31$ ($$( 1 + 4 T + 58 T^{2} + 124 T^{3} + 961 T^{4} )^{2}$$)($$( 1 - 8 T + 60 T^{2} - 248 T^{3} + 961 T^{4} )^{2}$$)($$( 1 - 8 T + 60 T^{2} - 248 T^{3} + 961 T^{4} )^{2}$$)($$( 1 + 4 T + 58 T^{2} + 124 T^{3} + 961 T^{4} )^{2}$$)
$37$ ($$( 1 - 6 T + 37 T^{2} )^{4}$$)($$( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 6 T + 37 T^{2} )^{4}$$)
$41$ ($$( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 12 T + 116 T^{2} + 492 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 12 T + 116 T^{2} - 492 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} )^{2}$$)
$43$ ($$1 - 76 T^{2} + 3094 T^{4} - 140524 T^{6} + 3418801 T^{8}$$)($$1 - 134 T^{2} + 8115 T^{4} - 247766 T^{6} + 3418801 T^{8}$$)($$1 - 134 T^{2} + 8115 T^{4} - 247766 T^{6} + 3418801 T^{8}$$)($$1 - 76 T^{2} + 3094 T^{4} - 140524 T^{6} + 3418801 T^{8}$$)
$47$ ($$1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8}$$)($$1 - 16 T^{2} - 2718 T^{4} - 35344 T^{6} + 4879681 T^{8}$$)($$1 - 16 T^{2} - 2718 T^{4} - 35344 T^{6} + 4879681 T^{8}$$)($$1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8}$$)
$53$ ($$1 - 188 T^{2} + 14326 T^{4} - 528092 T^{6} + 7890481 T^{8}$$)($$1 - 190 T^{2} + 14571 T^{4} - 533710 T^{6} + 7890481 T^{8}$$)($$1 - 190 T^{2} + 14571 T^{4} - 533710 T^{6} + 7890481 T^{8}$$)($$1 - 188 T^{2} + 14326 T^{4} - 528092 T^{6} + 7890481 T^{8}$$)
$59$ ($$1 - 100 T^{2} + 4854 T^{4} - 348100 T^{6} + 12117361 T^{8}$$)($$1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8}$$)($$1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8}$$)($$1 - 100 T^{2} + 4854 T^{4} - 348100 T^{6} + 12117361 T^{8}$$)
$61$ ($$1 - 100 T^{2} + 7894 T^{4} - 372100 T^{6} + 13845841 T^{8}$$)($$1 - 158 T^{2} + 11883 T^{4} - 587918 T^{6} + 13845841 T^{8}$$)($$1 - 158 T^{2} + 11883 T^{4} - 587918 T^{6} + 13845841 T^{8}$$)($$1 - 100 T^{2} + 7894 T^{4} - 372100 T^{6} + 13845841 T^{8}$$)
$67$ ($$( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 + 8 T + 78 T^{2} + 536 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 + 8 T + 78 T^{2} + 536 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} )^{2}$$)
$71$ ($$1 - 148 T^{2} + 10950 T^{4} - 746068 T^{6} + 25411681 T^{8}$$)($$1 - 176 T^{2} + 15234 T^{4} - 887216 T^{6} + 25411681 T^{8}$$)($$1 - 176 T^{2} + 15234 T^{4} - 887216 T^{6} + 25411681 T^{8}$$)($$1 - 148 T^{2} + 10950 T^{4} - 746068 T^{6} + 25411681 T^{8}$$)
$73$ ($$( 1 - 2 T^{2} + 5329 T^{4} )^{2}$$)($$1 - 140 T^{2} + 14406 T^{4} - 746060 T^{6} + 28398241 T^{8}$$)($$1 - 140 T^{2} + 14406 T^{4} - 746060 T^{6} + 28398241 T^{8}$$)($$( 1 - 2 T^{2} + 5329 T^{4} )^{2}$$)
$79$ ($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}$$)($$1 - 272 T^{2} + 30690 T^{4} - 1697552 T^{6} + 38950081 T^{8}$$)($$1 - 272 T^{2} + 30690 T^{4} - 1697552 T^{6} + 38950081 T^{8}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}$$)
$83$ ($$( 1 - 12 T + 83 T^{2} )^{4}$$)($$( 1 - 6 T - 25 T^{2} - 498 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 6 T - 25 T^{2} + 498 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 12 T + 83 T^{2} )^{4}$$)
$89$ ($$1 - 284 T^{2} + 35494 T^{4} - 2249564 T^{6} + 62742241 T^{8}$$)($$1 + 98 T^{2} + 16443 T^{4} + 776258 T^{6} + 62742241 T^{8}$$)($$1 + 98 T^{2} + 16443 T^{4} + 776258 T^{6} + 62742241 T^{8}$$)($$1 - 284 T^{2} + 35494 T^{4} - 2249564 T^{6} + 62742241 T^{8}$$)
$97$ ($$( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 7 T + 97 T^{2} )^{4}$$)($$( 1 + 7 T + 97 T^{2} )^{4}$$)($$( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2}$$)