# Properties

 Label 105.2.b Level 105 Weight 2 Character orbit b Rep. character $$\chi_{105}(41,\cdot)$$ Character field $$\Q$$ Dimension 12 Newform subspaces 4 Sturm bound 32 Trace bound 5

# Related objects

## Defining parameters

 Level: $$N$$ = $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 105.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$21$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$32$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$17$$

## Dimensions

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

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

## Trace form

 $$12q - 16q^{4} - 8q^{7} - 2q^{9} + O(q^{10})$$ $$12q - 16q^{4} - 8q^{7} - 2q^{9} + 2q^{15} + 8q^{16} - 4q^{18} + 6q^{21} + 8q^{22} + 12q^{25} + 16q^{28} + 4q^{30} - 36q^{36} - 16q^{37} + 30q^{39} + 36q^{42} - 40q^{43} - 16q^{46} + 12q^{49} - 30q^{51} - 12q^{57} + 8q^{58} - 36q^{60} - 44q^{63} - 8q^{64} + 24q^{67} + 64q^{72} + 84q^{78} + 36q^{79} + 22q^{81} - 36q^{84} - 12q^{85} + 16q^{88} - 12q^{91} + 12q^{93} + 26q^{99} + O(q^{100})$$

## 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.b.a $$2$$ $$0.838$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$4$$ $$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots$$
105.2.b.b $$2$$ $$0.838$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$4$$ $$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots$$
105.2.b.c $$4$$ $$0.838$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-1$$ $$-4$$ $$-8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots$$
105.2.b.d $$4$$ $$0.838$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$4$$ $$-8$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 - T^{2} + 4 T^{4}$$)($$1 - T^{2} + 4 T^{4}$$)($$1 - T^{2} - 4 T^{6} + 16 T^{8}$$)($$1 - T^{2} - 4 T^{6} + 16 T^{8}$$)
$3$ ($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$$)($$1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4}$$)
$5$ ($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 - T )^{4}$$)
$7$ ($$1 - 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$( 1 + 4 T + 7 T^{2} )^{2}$$)($$( 1 + 4 T + 7 T^{2} )^{2}$$)
$11$ ($$1 - 10 T^{2} + 121 T^{4}$$)($$1 - 10 T^{2} + 121 T^{4}$$)($$1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8}$$)($$1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8}$$)
$13$ ($$( 1 - 13 T^{2} )^{2}$$)($$( 1 - 13 T^{2} )^{2}$$)($$1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8}$$)($$1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8}$$)
$17$ ($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 3 T + 28 T^{2} + 51 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 3 T + 28 T^{2} - 51 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)
$23$ ($$1 - 34 T^{2} + 529 T^{4}$$)($$1 - 34 T^{2} + 529 T^{4}$$)($$1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8}$$)($$1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8}$$)
$29$ ($$1 - 10 T^{2} + 841 T^{4}$$)($$1 - 10 T^{2} + 841 T^{4}$$)($$1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8}$$)($$1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8}$$)
$31$ ($$1 - 50 T^{2} + 961 T^{4}$$)($$1 - 50 T^{2} + 961 T^{4}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)
$37$ ($$( 1 + 2 T + 37 T^{2} )^{2}$$)($$( 1 + 2 T + 37 T^{2} )^{2}$$)($$( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2}$$)
$41$ ($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{4}$$)($$( 1 + 6 T + 41 T^{2} )^{4}$$)
$43$ ($$( 1 + 8 T + 43 T^{2} )^{2}$$)($$( 1 + 8 T + 43 T^{2} )^{2}$$)($$( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2}$$)
$47$ ($$( 1 + 12 T + 47 T^{2} )^{2}$$)($$( 1 - 12 T + 47 T^{2} )^{2}$$)($$( 1 - 9 T + 106 T^{2} - 423 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 9 T + 106 T^{2} + 423 T^{3} + 2209 T^{4} )^{2}$$)
$53$ ($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8}$$)($$1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8}$$)
$59$ ($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 94 T^{2} - 354 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 + 6 T + 94 T^{2} + 354 T^{3} + 3481 T^{4} )^{2}$$)
$61$ ($$( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} )$$)($$( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} )$$)($$( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2}$$)
$67$ ($$( 1 - 8 T + 67 T^{2} )^{2}$$)($$( 1 - 8 T + 67 T^{2} )^{2}$$)($$( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2}$$)
$71$ ($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8}$$)($$1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8}$$)
$73$ ($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$( 1 - 98 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 98 T^{2} + 5329 T^{4} )^{2}$$)
$79$ ($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2}$$)
$83$ ($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 - 12 T + 70 T^{2} - 996 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 12 T + 70 T^{2} + 996 T^{3} + 6889 T^{4} )^{2}$$)
$89$ ($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 + 18 T + 226 T^{2} + 1602 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 18 T + 226 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2}$$)
$97$ ($$1 - 146 T^{2} + 9409 T^{4}$$)($$1 - 146 T^{2} + 9409 T^{4}$$)($$1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8}$$)($$1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8}$$)