# Properties

 Label 105.2.g Level 105 Weight 2 Character orbit g Rep. character $$\chi_{105}(104,\cdot)$$ Character field $$\Q$$ Dimension 12 Newform subspaces 3 Sturm bound 32 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 105.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$105$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$32$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(105, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12q - 6q^{9} + O(q^{10})$$ $$12q - 6q^{9} + 6q^{15} - 24q^{16} + 6q^{21} - 12q^{25} - 24q^{30} - 12q^{36} + 18q^{39} + 48q^{46} - 12q^{49} + 42q^{51} + 36q^{60} - 24q^{64} + 24q^{70} + 60q^{79} - 90q^{81} - 36q^{84} - 12q^{85} - 60q^{91} + 6q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.2.g.a $$4$$ $$0.838$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$-4$$ $$0$$ $$4$$ $$q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
105.2.g.b $$4$$ $$0.838$$ $$\Q(\sqrt{-5}, \sqrt{7})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
105.2.g.c $$4$$ $$0.838$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T^{2} + 4 T^{4} )^{2}$$)($$( 1 + 2 T^{2} )^{4}$$)($$( 1 + T^{2} + 4 T^{4} )^{2}$$)
$3$ ($$( 1 + 2 T + 3 T^{2} )^{2}$$)($$1 - T^{2} + 9 T^{4}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)
$5$ ($$1 - 2 T^{2} + 25 T^{4}$$)($$( 1 + 5 T^{2} )^{2}$$)($$1 - 2 T^{2} + 25 T^{4}$$)
$7$ ($$( 1 - 2 T + 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 + 2 T + 7 T^{2} )^{2}$$)
$11$ ($$( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 - 3 T + 11 T^{2} )^{2}( 1 + 3 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2}$$)
$13$ ($$( 1 + 4 T + 13 T^{2} )^{4}$$)($$( 1 + 19 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 4 T + 13 T^{2} )^{4}$$)
$17$ ($$( 1 - 26 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 29 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 26 T^{2} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 19 T^{2} )^{4}$$)($$( 1 - 19 T^{2} )^{4}$$)($$( 1 - 19 T^{2} )^{4}$$)
$23$ ($$( 1 + 34 T^{2} + 529 T^{4} )^{2}$$)($$( 1 + 23 T^{2} )^{4}$$)($$( 1 + 34 T^{2} + 529 T^{4} )^{2}$$)
$29$ ($$( 1 - 26 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 9 T + 29 T^{2} )^{2}( 1 + 9 T + 29 T^{2} )^{2}$$)($$( 1 - 26 T^{2} + 841 T^{4} )^{2}$$)
$31$ ($$( 1 + 34 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 31 T^{2} )^{4}$$)($$( 1 + 34 T^{2} + 961 T^{4} )^{2}$$)
$37$ ($$( 1 - 37 T^{2} )^{4}$$)($$( 1 - 37 T^{2} )^{4}$$)($$( 1 - 37 T^{2} )^{4}$$)
$41$ ($$( 1 + 70 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 41 T^{2} )^{4}$$)($$( 1 + 70 T^{2} + 1681 T^{4} )^{2}$$)
$43$ ($$( 1 - 62 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 - 62 T^{2} + 1849 T^{4} )^{2}$$)
$47$ ($$( 1 - 86 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 31 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 86 T^{2} + 2209 T^{4} )^{2}$$)
$53$ ($$( 1 + 53 T^{2} )^{4}$$)($$( 1 + 53 T^{2} )^{4}$$)($$( 1 + 53 T^{2} )^{4}$$)
$59$ ($$( 1 + 70 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 70 T^{2} + 3481 T^{4} )^{2}$$)
$61$ ($$( 1 - 26 T^{2} + 3721 T^{4} )^{2}$$)($$( 1 - 61 T^{2} )^{4}$$)($$( 1 - 26 T^{2} + 3721 T^{4} )^{2}$$)
$67$ ($$( 1 - 110 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 67 T^{2} )^{4}$$)($$( 1 - 110 T^{2} + 4489 T^{4} )^{2}$$)
$71$ ($$( 1 - 134 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 - 134 T^{2} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 - 8 T + 73 T^{2} )^{4}$$)($$( 1 + 34 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 8 T + 73 T^{2} )^{4}$$)
$79$ ($$( 1 - 8 T + 79 T^{2} )^{4}$$)($$( 1 + T + 79 T^{2} )^{4}$$)($$( 1 - 8 T + 79 T^{2} )^{4}$$)
$83$ ($$( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2}$$)($$( 1 - 86 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2}$$)
$89$ ($$( 1 + 70 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 70 T^{2} + 7921 T^{4} )^{2}$$)
$97$ ($$( 1 - 8 T + 97 T^{2} )^{4}$$)($$( 1 - 149 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 8 T + 97 T^{2} )^{4}$$)