Properties

Label 272.4.a
Level 272272
Weight 44
Character orbit 272.a
Rep. character χ272(1,)\chi_{272}(1,\cdot)
Character field Q\Q
Dimension 2424
Newform subspaces 1111
Sturm bound 144144
Trace bound 55

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 272=2417 272 = 2^{4} \cdot 17
Weight: k k == 4 4
Character orbit: [χ][\chi] == 272.a (trivial)
Character field: Q\Q
Newform subspaces: 11 11
Sturm bound: 144144
Trace bound: 55
Distinguishing TpT_p: 33, 55

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ0(272))M_{4}(\Gamma_0(272)).

Total New Old
Modular forms 114 24 90
Cusp forms 102 24 78
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

221717FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++31317724242828772121330033
++--27275522222424551919330033
-++-26265521212323551818330033
--++30307723232727772020330033
Plus space++616114144747555514144141660066
Minus space-535310104343474710103737660066

Trace form

24q6q3+50q7+216q986q11+12q15+180q19+136q2126q23+768q25+360q27256q2954q3124q33+228q358q37+432q39+296q41+26q99+O(q100) 24 q - 6 q^{3} + 50 q^{7} + 216 q^{9} - 86 q^{11} + 12 q^{15} + 180 q^{19} + 136 q^{21} - 26 q^{23} + 768 q^{25} + 360 q^{27} - 256 q^{29} - 54 q^{31} - 24 q^{33} + 228 q^{35} - 8 q^{37} + 432 q^{39} + 296 q^{41}+ \cdots - 26 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ0(272))S_{4}^{\mathrm{new}}(\Gamma_0(272)) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces A-L signs Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7} 2 17
272.4.a.a 272.a 1.a 11 16.04916.049 Q\Q None 34.4.a.a 00 22 18-18 1010 - - SU(2)\mathrm{SU}(2) q+2q318q5+10q723q9+6q11+q+2q^{3}-18q^{5}+10q^{7}-23q^{9}+6q^{11}+\cdots
272.4.a.b 272.a 1.a 11 16.04916.049 Q\Q None 68.4.a.a 00 22 8-8 1212 - ++ SU(2)\mathrm{SU}(2) q+2q38q5+12q723q9+10q11+q+2q^{3}-8q^{5}+12q^{7}-23q^{9}+10q^{11}+\cdots
272.4.a.c 272.a 1.a 11 16.04916.049 Q\Q None 34.4.a.b 00 22 1616 24-24 - ++ SU(2)\mathrm{SU}(2) q+2q3+24q524q723q962q11+q+2q^{3}+2^{4}q^{5}-24q^{7}-23q^{9}-62q^{11}+\cdots
272.4.a.d 272.a 1.a 11 16.04916.049 Q\Q None 17.4.a.a 00 88 66 2828 - - SU(2)\mathrm{SU}(2) q+8q3+6q5+28q7+37q9+24q11+q+8q^{3}+6q^{5}+28q^{7}+37q^{9}+24q^{11}+\cdots
272.4.a.e 272.a 1.a 22 16.04916.049 Q(13)\Q(\sqrt{13}) None 34.4.a.c 00 6-6 4-4 66 - - SU(2)\mathrm{SU}(2) q+(3β)q3+(24β)q5+(3+β)q7+q+(-3-\beta )q^{3}+(-2-4\beta )q^{5}+(3+\beta )q^{7}+\cdots
272.4.a.f 272.a 1.a 22 16.04916.049 Q(3)\Q(\sqrt{3}) None 136.4.a.a 00 4-4 12-12 3636 ++ - SU(2)\mathrm{SU}(2) q+(2+β)q3+(6+2β)q5+(18+)q7+q+(-2+\beta )q^{3}+(-6+2\beta )q^{5}+(18+\cdots)q^{7}+\cdots
272.4.a.g 272.a 1.a 33 16.04916.049 3.3.1556.1 None 136.4.a.c 00 8-8 22 12-12 ++ - SU(2)\mathrm{SU}(2) q+(3+β2)q3+(1β1)q5+(4+)q7+q+(-3+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(-4+\cdots)q^{7}+\cdots
272.4.a.h 272.a 1.a 33 16.04916.049 3.3.2636.1 None 17.4.a.b 00 4-4 8-8 22-22 - ++ SU(2)\mathrm{SU}(2) q+(1+β1β2)q3+(3+β2)q5+q+(-1+\beta _{1}-\beta _{2})q^{3}+(-3+\beta _{2})q^{5}+\cdots
272.4.a.i 272.a 1.a 33 16.04916.049 3.3.1524.1 None 68.4.a.b 00 4-4 2626 8-8 - - SU(2)\mathrm{SU}(2) q+(1β2)q3+(9β1)q5+(2+)q7+q+(-1-\beta _{2})q^{3}+(9-\beta _{1})q^{5}+(-2+\cdots)q^{7}+\cdots
272.4.a.j 272.a 1.a 33 16.04916.049 3.3.8396.1 None 136.4.a.b 00 44 8-8 22 ++ ++ SU(2)\mathrm{SU}(2) q+(1β2)q3+(3+β12β2)q5+q+(1-\beta _{2})q^{3}+(-3+\beta _{1}-2\beta _{2})q^{5}+\cdots
272.4.a.k 272.a 1.a 44 16.04916.049 4.4.550476.1 None 136.4.a.d 00 22 88 2222 ++ ++ SU(2)\mathrm{SU}(2) q+β1q3+(1β1β22β3)q5+q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots

Decomposition of S4old(Γ0(272))S_{4}^{\mathrm{old}}(\Gamma_0(272)) into lower level spaces