# Properties

 Label 15.3.d Level 15 Weight 3 Character orbit d Rep. character $$\chi_{15}(14,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 2 Sturm bound 6 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$15 = 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 15.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$6$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(15, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

## Trace form

 $$2q - 6q^{4} - 6q^{6} + 18q^{9} + O(q^{10})$$ $$2q - 6q^{4} - 6q^{6} + 18q^{9} + 10q^{10} - 30q^{15} + 10q^{16} - 44q^{19} + 42q^{24} + 50q^{25} + 4q^{31} - 28q^{34} - 54q^{36} - 70q^{40} + 68q^{46} + 98q^{49} + 84q^{51} - 54q^{54} + 90q^{60} - 236q^{61} + 26q^{64} - 204q^{69} + 132q^{76} + 196q^{79} + 162q^{81} - 140q^{85} + 90q^{90} - 28q^{94} - 198q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(15, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
15.3.d.a $$1$$ $$0.409$$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$-1$$ $$3$$ $$-5$$ $$0$$ $$q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots$$
15.3.d.b $$1$$ $$0.409$$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$1$$ $$-3$$ $$5$$ $$0$$ $$q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + T + 4 T^{2}$$)($$1 - T + 4 T^{2}$$)
$3$ ($$1 - 3 T$$)($$1 + 3 T$$)
$5$ ($$1 + 5 T$$)($$1 - 5 T$$)
$7$ ($$( 1 - 7 T )( 1 + 7 T )$$)($$( 1 - 7 T )( 1 + 7 T )$$)
$11$ ($$( 1 - 11 T )( 1 + 11 T )$$)($$( 1 - 11 T )( 1 + 11 T )$$)
$13$ ($$( 1 - 13 T )( 1 + 13 T )$$)($$( 1 - 13 T )( 1 + 13 T )$$)
$17$ ($$1 - 14 T + 289 T^{2}$$)($$1 + 14 T + 289 T^{2}$$)
$19$ ($$1 + 22 T + 361 T^{2}$$)($$1 + 22 T + 361 T^{2}$$)
$23$ ($$1 + 34 T + 529 T^{2}$$)($$1 - 34 T + 529 T^{2}$$)
$29$ ($$( 1 - 29 T )( 1 + 29 T )$$)($$( 1 - 29 T )( 1 + 29 T )$$)
$31$ ($$1 - 2 T + 961 T^{2}$$)($$1 - 2 T + 961 T^{2}$$)
$37$ ($$( 1 - 37 T )( 1 + 37 T )$$)($$( 1 - 37 T )( 1 + 37 T )$$)
$41$ ($$( 1 - 41 T )( 1 + 41 T )$$)($$( 1 - 41 T )( 1 + 41 T )$$)
$43$ ($$( 1 - 43 T )( 1 + 43 T )$$)($$( 1 - 43 T )( 1 + 43 T )$$)
$47$ ($$1 - 14 T + 2209 T^{2}$$)($$1 + 14 T + 2209 T^{2}$$)
$53$ ($$1 - 86 T + 2809 T^{2}$$)($$1 + 86 T + 2809 T^{2}$$)
$59$ ($$( 1 - 59 T )( 1 + 59 T )$$)($$( 1 - 59 T )( 1 + 59 T )$$)
$61$ ($$1 + 118 T + 3721 T^{2}$$)($$1 + 118 T + 3721 T^{2}$$)
$67$ ($$( 1 - 67 T )( 1 + 67 T )$$)($$( 1 - 67 T )( 1 + 67 T )$$)
$71$ ($$( 1 - 71 T )( 1 + 71 T )$$)($$( 1 - 71 T )( 1 + 71 T )$$)
$73$ ($$( 1 - 73 T )( 1 + 73 T )$$)($$( 1 - 73 T )( 1 + 73 T )$$)
$79$ ($$1 - 98 T + 6241 T^{2}$$)($$1 - 98 T + 6241 T^{2}$$)
$83$ ($$1 + 154 T + 6889 T^{2}$$)($$1 - 154 T + 6889 T^{2}$$)
$89$ ($$( 1 - 89 T )( 1 + 89 T )$$)($$( 1 - 89 T )( 1 + 89 T )$$)
$97$ ($$( 1 - 97 T )( 1 + 97 T )$$)($$( 1 - 97 T )( 1 + 97 T )$$)