# Properties

 Label 2015.1.h Level 2015 Weight 1 Character orbit h Rep. character $$\chi_{2015}(2014,\cdot)$$ Character field $$\Q$$ Dimension 28 Newform subspaces 5 Sturm bound 224 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2015 = 5 \cdot 13 \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2015.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2015$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$224$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2015, [\chi])$$.

Total New Old
Modular forms 32 32 0
Cusp forms 28 28 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 28 0 0 0

## Trace form

 $$28q + 16q^{4} + 24q^{9} + O(q^{10})$$ $$28q + 16q^{4} + 24q^{9} - 4q^{10} - 8q^{14} + 20q^{16} + 20q^{25} - 4q^{35} + 4q^{36} - 8q^{40} + 16q^{49} - 16q^{56} + 8q^{64} - 16q^{66} - 16q^{69} + 12q^{81} - 12q^{90} - 8q^{94} - 8q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2015, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2015.1.h.a $$4$$ $$1.006$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots$$
2015.1.h.b $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ None $$-1$$ $$-1$$ $$6$$ $$-1$$ $$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$$
2015.1.h.c $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ None $$-1$$ $$1$$ $$6$$ $$-1$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$$
2015.1.h.d $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ None $$1$$ $$-1$$ $$-6$$ $$1$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
2015.1.h.e $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ None $$1$$ $$1$$ $$-6$$ $$1$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$3$ ($$( 1 + T^{4} )^{2}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$5$ ($$( 1 + T^{2} )^{2}$$)($$( 1 - T )^{6}$$)($$( 1 - T )^{6}$$)($$( 1 + T )^{6}$$)($$( 1 + T )^{6}$$)
$7$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$11$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)
$13$ ($$1 + T^{4}$$)($$( 1 - T )^{6}$$)($$( 1 + T )^{6}$$)($$( 1 - T )^{6}$$)($$( 1 + T )^{6}$$)
$17$ ($$( 1 + T^{4} )^{2}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$19$ ($$( 1 + T^{2} )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$23$ ($$( 1 + T^{4} )^{2}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$29$ ($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$31$ ($$( 1 + T^{2} )^{2}$$)($$( 1 - T )^{6}$$)($$( 1 + T )^{6}$$)($$( 1 + T )^{6}$$)($$( 1 - T )^{6}$$)
$37$ ($$( 1 + T^{4} )^{2}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$41$ ($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$43$ ($$( 1 + T^{4} )^{2}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$47$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$53$ ($$( 1 + T^{4} )^{2}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$59$ ($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$61$ ($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$67$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)
$71$ ($$( 1 + T^{2} )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$73$ ($$( 1 + T^{4} )^{2}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$79$ ($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$83$ ($$( 1 + T^{4} )^{2}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)($$( 1 - T )^{6}( 1 + T )^{6}$$)
$89$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)
$97$ ($$( 1 + T^{2} )^{4}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12}$$)