# Properties

 Label 105.3.k Level 105 Weight 3 Character orbit k Rep. character $$\chi_{105}(62,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 56 Newform subspaces 4 Sturm bound 48 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(105, [\chi])$$.

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

## Trace form

 $$56q + 4q^{7} + O(q^{10})$$ $$56q + 4q^{7} + 8q^{15} - 144q^{16} - 52q^{18} - 12q^{21} + 104q^{22} - 40q^{25} + 76q^{28} - 220q^{30} + 344q^{36} - 72q^{37} + 160q^{42} + 24q^{43} + 80q^{46} - 188q^{51} - 500q^{57} - 640q^{58} + 520q^{60} - 96q^{63} - 72q^{67} - 76q^{70} + 272q^{72} + 140q^{78} - 188q^{81} + 96q^{85} + 1344q^{88} + 424q^{91} + 548q^{93} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.3.k.a $$4$$ $$2.861$$ $$\Q(\zeta_{8})$$ None $$0$$ $$-8$$ $$0$$ $$-28$$ $$q+\zeta_{8}q^{2}+(-2-\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots$$
105.3.k.b $$4$$ $$2.861$$ $$\Q(\zeta_{8})$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(2+\zeta_{8}-2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots$$
105.3.k.c $$16$$ $$2.861$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$32$$ $$q-\beta _{1}q^{2}+(\beta _{7}+\beta _{10}-\beta _{13}+\beta _{15})q^{3}+\cdots$$
105.3.k.d $$32$$ $$2.861$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 17 T^{4} + 256 T^{8}$$)($$1 + 17 T^{4} + 256 T^{8}$$)($$( 1 + 17 T^{4} + 256 T^{8} )^{4}$$)
$3$ ($$1 + 8 T + 32 T^{2} + 72 T^{3} + 81 T^{4}$$)($$1 - 8 T + 32 T^{2} - 72 T^{3} + 81 T^{4}$$)($$1 - 224 T^{4} + 23490 T^{8} - 1469664 T^{12} + 43046721 T^{16}$$)
$5$ ($$1 + 48 T^{2} + 625 T^{4}$$)($$1 + 48 T^{2} + 625 T^{4}$$)($$( 1 - 56 T^{2} + 2000 T^{4} - 35000 T^{6} + 390625 T^{8} )^{2}$$)
$7$ ($$( 1 + 7 T )^{4}$$)($$( 1 + 49 T^{2} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 208 T^{3} - 958 T^{4} - 10192 T^{5} + 307328 T^{6} - 1882384 T^{7} + 5764801 T^{8} )^{2}$$)
$11$ ($$( 1 - 144 T^{2} + 14641 T^{4} )^{2}$$)($$( 1 - 144 T^{2} + 14641 T^{4} )^{2}$$)($$( 1 - 284 T^{2} + 40742 T^{4} - 4158044 T^{6} + 214358881 T^{8} )^{4}$$)
$13$ ($$( 1 + 16 T + 128 T^{2} + 2704 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 - 74400 T^{4} + 2876017858 T^{8} - 60690365642400 T^{12} + 665416609183179841 T^{16} )^{2}$$)
$17$ ($$1 - 157438 T^{4} + 6975757441 T^{8}$$)($$1 - 157438 T^{4} + 6975757441 T^{8}$$)($$( 1 + 280836 T^{4} + 33000880390 T^{8} + 1959043816700676 T^{12} + 48661191875666868481 T^{16} )^{2}$$)
$19$ ($$( 1 - 10 T + 361 T^{2} )^{4}$$)($$( 1 + 10 T + 361 T^{2} )^{4}$$)($$( 1 + 696 T^{2} + 371920 T^{4} + 90703416 T^{6} + 16983563041 T^{8} )^{4}$$)
$23$ ($$1 - 550078 T^{4} + 78310985281 T^{8}$$)($$1 - 550078 T^{4} + 78310985281 T^{8}$$)($$( 1 + 107644 T^{4} - 83134815354 T^{8} + 8429707699587964 T^{12} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)
$29$ ($$( 1 + 1664 T^{2} + 707281 T^{4} )^{2}$$)($$( 1 + 1664 T^{2} + 707281 T^{4} )^{2}$$)($$( 1 + 2444 T^{2} + 2801222 T^{4} + 1728594764 T^{6} + 500246412961 T^{8} )^{4}$$)
$31$ ($$( 1 - 1726 T^{2} + 923521 T^{4} )^{2}$$)($$( 1 - 1726 T^{2} + 923521 T^{4} )^{2}$$)($$( 1 - 2596 T^{2} + 3425222 T^{4} - 2397460516 T^{6} + 852891037441 T^{8} )^{4}$$)
$37$ ($$( 1 - 60 T + 1800 T^{2} - 82140 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 - 60 T + 1800 T^{2} - 82140 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 + 96 T + 4608 T^{2} + 183264 T^{3} + 6996962 T^{4} + 250888416 T^{5} + 8636133888 T^{6} + 246309735264 T^{7} + 3512479453921 T^{8} )^{4}$$)
$41$ ($$( 1 + 2210 T^{2} + 2825761 T^{4} )^{2}$$)($$( 1 + 2210 T^{2} + 2825761 T^{4} )^{2}$$)($$( 1 + 5716 T^{2} + 13775622 T^{4} + 16152049876 T^{6} + 7984925229121 T^{8} )^{4}$$)
$43$ ($$( 1 - 72 T + 2592 T^{2} - 133128 T^{3} + 3418801 T^{4} )^{2}$$)($$( 1 - 72 T + 2592 T^{2} - 133128 T^{3} + 3418801 T^{4} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 2896 T^{3} - 2716702 T^{4} - 5354704 T^{5} + 437606528 T^{6} - 101141808784 T^{7} + 11688200277601 T^{8} )^{4}$$)
$47$ ($$1 + 9442562 T^{4} + 23811286661761 T^{8}$$)($$1 + 9442562 T^{4} + 23811286661761 T^{8}$$)($$( 1 - 5511420 T^{4} + 7619082080518 T^{8} -$$$$13\!\cdots\!20$$$$T^{12} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)
$53$ ($$1 + 3420962 T^{4} + 62259690411361 T^{8}$$)($$1 + 3420962 T^{4} + 62259690411361 T^{8}$$)($$( 1 - 19870076 T^{4} + 198820934324166 T^{8} -$$$$12\!\cdots\!36$$$$T^{12} +$$$$38\!\cdots\!21$$$$T^{16} )^{2}$$)
$59$ ($$( 1 - 6080 T^{2} + 12117361 T^{4} )^{2}$$)($$( 1 - 6080 T^{2} + 12117361 T^{4} )^{2}$$)($$( 1 - 10776 T^{2} + 52783792 T^{4} - 130576682136 T^{6} + 146830437604321 T^{8} )^{4}$$)
$61$ ($$( 1 - 7246 T^{2} + 13845841 T^{4} )^{2}$$)($$( 1 - 7246 T^{2} + 13845841 T^{4} )^{2}$$)($$( 1 - 8200 T^{2} + 36103376 T^{4} - 113535896200 T^{6} + 191707312997281 T^{8} )^{4}$$)
$67$ ($$( 1 - 64 T + 2048 T^{2} - 287296 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 64 T + 2048 T^{2} - 287296 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 80 T + 3200 T^{2} + 17520 T^{3} - 22069342 T^{4} + 78647280 T^{5} + 64483587200 T^{6} - 7236670573520 T^{7} + 406067677556641 T^{8} )^{4}$$)
$71$ ($$( 1 - 6554 T^{2} + 25411681 T^{4} )^{2}$$)($$( 1 - 6554 T^{2} + 25411681 T^{4} )^{2}$$)($$( 1 - 17504 T^{2} + 126269762 T^{4} - 444806064224 T^{6} + 645753531245761 T^{8} )^{4}$$)
$73$ ($$( 1 + 78 T + 3042 T^{2} + 415662 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 78 T + 3042 T^{2} - 415662 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 10432892 T^{4} + 418480444620678 T^{8} -$$$$84\!\cdots\!52$$$$T^{12} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)
$79$ ($$( 1 - 9346 T^{2} + 38950081 T^{4} )^{2}$$)($$( 1 - 9346 T^{2} + 38950081 T^{4} )^{2}$$)($$( 1 - 6736 T^{2} + 38950081 T^{4} )^{8}$$)
$83$ ($$1 + 27716834 T^{4} + 2252292232139041 T^{8}$$)($$1 + 27716834 T^{4} + 2252292232139041 T^{8}$$)($$( 1 - 55419104 T^{4} + 5263624308845250 T^{8} -$$$$12\!\cdots\!64$$$$T^{12} +$$$$50\!\cdots\!81$$$$T^{16} )^{2}$$)
$89$ ($$( 1 - 15450 T^{2} + 62742241 T^{4} )^{2}$$)($$( 1 - 15450 T^{2} + 62742241 T^{4} )^{2}$$)($$( 1 - 1108 T^{2} - 101931898 T^{4} - 69518403028 T^{6} + 3936588805702081 T^{8} )^{4}$$)
$97$ ($$( 1 + 226 T + 25538 T^{2} + 2126434 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 226 T + 25538 T^{2} - 2126434 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 284585220 T^{4} + 35721324461420038 T^{8} +$$$$22\!\cdots\!20$$$$T^{12} +$$$$61\!\cdots\!21$$$$T^{16} )^{2}$$)