# Properties

 Label 15.5.d Level 15 Weight 5 Character orbit d Rep. character $$\chi_{15}(14,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 3 Sturm bound 10 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$15 = 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 15.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$10$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(15, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q + 42q^{4} - 66q^{6} + 18q^{9} + O(q^{10})$$ $$6q + 42q^{4} - 66q^{6} + 18q^{9} - 270q^{10} + 570q^{15} + 114q^{16} + 756q^{19} + 468q^{21} - 3462q^{24} - 930q^{25} + 2340q^{30} - 3708q^{31} + 8868q^{34} + 6210q^{36} - 7488q^{39} - 7710q^{40} + 7020q^{45} - 6612q^{46} + 13470q^{49} - 1596q^{51} - 19386q^{54} - 9360q^{55} + 14130q^{60} + 9252q^{61} + 10530q^{64} + 9360q^{66} - 6096q^{69} - 4680q^{70} + 9360q^{75} - 23100q^{76} - 5724q^{79} - 2754q^{81} - 2808q^{84} - 12060q^{85} - 31230q^{90} + 14976q^{91} + 28188q^{94} + 9522q^{96} + 28080q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(15, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
15.5.d.a $$1$$ $$1.551$$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$-7$$ $$9$$ $$25$$ $$0$$ $$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$$
15.5.d.b $$1$$ $$1.551$$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$7$$ $$-9$$ $$-25$$ $$0$$ $$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$$
15.5.d.c $$4$$ $$1.551$$ $$\Q(\sqrt{10}, \sqrt{-26})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 7 T + 16 T^{2}$$)($$1 - 7 T + 16 T^{2}$$)($$( 1 + 22 T^{2} + 256 T^{4} )^{2}$$)
$3$ ($$1 - 9 T$$)($$1 + 9 T$$)($$1 + 72 T^{2} + 6561 T^{4}$$)
$5$ ($$1 - 25 T$$)($$1 + 25 T$$)($$1 + 1090 T^{2} + 390625 T^{4}$$)
$7$ ($$( 1 - 49 T )( 1 + 49 T )$$)($$( 1 - 49 T )( 1 + 49 T )$$)($$( 1 - 4568 T^{2} + 5764801 T^{4} )^{2}$$)
$11$ ($$( 1 - 121 T )( 1 + 121 T )$$)($$( 1 - 121 T )( 1 + 121 T )$$)($$( 1 - 19922 T^{2} + 214358881 T^{4} )^{2}$$)
$13$ ($$( 1 - 169 T )( 1 + 169 T )$$)($$( 1 - 169 T )( 1 + 169 T )$$)($$( 1 + 2782 T^{2} + 815730721 T^{4} )^{2}$$)
$17$ ($$1 + 382 T + 83521 T^{2}$$)($$1 - 382 T + 83521 T^{2}$$)($$( 1 + 89602 T^{2} + 6975757441 T^{4} )^{2}$$)
$19$ ($$1 + 238 T + 130321 T^{2}$$)($$1 + 238 T + 130321 T^{2}$$)($$( 1 - 308 T + 130321 T^{2} )^{4}$$)
$23$ ($$1 - 98 T + 279841 T^{2}$$)($$1 + 98 T + 279841 T^{2}$$)($$( 1 + 388072 T^{2} + 78310985281 T^{4} )^{2}$$)
$29$ ($$( 1 - 841 T )( 1 + 841 T )$$)($$( 1 - 841 T )( 1 + 841 T )$$)($$( 1 - 1377122 T^{2} + 500246412961 T^{4} )^{2}$$)
$31$ ($$1 + 1918 T + 923521 T^{2}$$)($$1 + 1918 T + 923521 T^{2}$$)($$( 1 - 32 T + 923521 T^{2} )^{4}$$)
$37$ ($$( 1 - 1369 T )( 1 + 1369 T )$$)($$( 1 - 1369 T )( 1 + 1369 T )$$)($$( 1 - 2097218 T^{2} + 3512479453921 T^{4} )^{2}$$)
$41$ ($$( 1 - 1681 T )( 1 + 1681 T )$$)($$( 1 - 1681 T )( 1 + 1681 T )$$)($$( 1 - 1324862 T^{2} + 7984925229121 T^{4} )^{2}$$)
$43$ ($$( 1 - 1849 T )( 1 + 1849 T )$$)($$( 1 - 1849 T )( 1 + 1849 T )$$)($$( 1 - 154328 T^{2} + 11688200277601 T^{4} )^{2}$$)
$47$ ($$1 + 4222 T + 4879681 T^{2}$$)($$1 - 4222 T + 4879681 T^{2}$$)($$( 1 + 3784072 T^{2} + 23811286661761 T^{4} )^{2}$$)
$53$ ($$1 - 1778 T + 7890481 T^{2}$$)($$1 + 1778 T + 7890481 T^{2}$$)($$( 1 + 13773922 T^{2} + 62259690411361 T^{4} )^{2}$$)
$59$ ($$( 1 - 3481 T )( 1 + 3481 T )$$)($$( 1 - 3481 T )( 1 + 3481 T )$$)($$( 1 - 8500562 T^{2} + 146830437604321 T^{4} )^{2}$$)
$61$ ($$1 - 6482 T + 13845841 T^{2}$$)($$1 - 6482 T + 13845841 T^{2}$$)($$( 1 + 928 T + 13845841 T^{2} )^{4}$$)
$67$ ($$( 1 - 4489 T )( 1 + 4489 T )$$)($$( 1 - 4489 T )( 1 + 4489 T )$$)($$( 1 - 33618968 T^{2} + 406067677556641 T^{4} )^{2}$$)
$71$ ($$( 1 - 5041 T )( 1 + 5041 T )$$)($$( 1 - 5041 T )( 1 + 5041 T )$$)($$( 1 - 29257922 T^{2} + 645753531245761 T^{4} )^{2}$$)
$73$ ($$( 1 - 5329 T )( 1 + 5329 T )$$)($$( 1 - 5329 T )( 1 + 5329 T )$$)($$( 1 - 38971298 T^{2} + 806460091894081 T^{4} )^{2}$$)
$79$ ($$1 + 2878 T + 38950081 T^{2}$$)($$1 + 2878 T + 38950081 T^{2}$$)($$( 1 - 8 T + 38950081 T^{2} )^{4}$$)
$83$ ($$1 - 9938 T + 47458321 T^{2}$$)($$1 + 9938 T + 47458321 T^{2}$$)($$( 1 + 75232552 T^{2} + 2252292232139041 T^{4} )^{2}$$)
$89$ ($$( 1 - 7921 T )( 1 + 7921 T )$$)($$( 1 - 7921 T )( 1 + 7921 T )$$)($$( 1 - 39222722 T^{2} + 3936588805702081 T^{4} )^{2}$$)
$97$ ($$( 1 - 9409 T )( 1 + 9409 T )$$)($$( 1 - 9409 T )( 1 + 9409 T )$$)($$( 1 - 170764898 T^{2} + 7837433594376961 T^{4} )^{2}$$)