Properties

Label 224.4.a
Level 224224
Weight 44
Character orbit 224.a
Rep. character χ224(1,)\chi_{224}(1,\cdot)
Character field Q\Q
Dimension 1818
Newform subspaces 88
Sturm bound 128128
Trace bound 77

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Defining parameters

Level: N N == 224=257 224 = 2^{5} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 224.a (trivial)
Character field: Q\Q
Newform subspaces: 8 8
Sturm bound: 128128
Trace bound: 77
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ0(224))M_{4}(\Gamma_0(224)).

Total New Old
Modular forms 104 18 86
Cusp forms 88 18 70
Eisenstein series 16 0 16

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

2277FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++29295524242525552020440044
++--23233320201919331616440044
-++-25254421212121441717440044
--++27276621212323661717440044
Plus space++565611114545484811113737880088
Minus space-48487741414040773333880088

Trace form

18q4q5+122q9+92q13+308q17+318q25+284q29+1232q33660q37588q41+1788q45+882q49+1388q53768q57+780q611304q651488q69+3628q97+O(q100) 18 q - 4 q^{5} + 122 q^{9} + 92 q^{13} + 308 q^{17} + 318 q^{25} + 284 q^{29} + 1232 q^{33} - 660 q^{37} - 588 q^{41} + 1788 q^{45} + 882 q^{49} + 1388 q^{53} - 768 q^{57} + 780 q^{61} - 1304 q^{65} - 1488 q^{69}+ \cdots - 3628 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ0(224))S_{4}^{\mathrm{new}}(\Gamma_0(224)) 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 7
224.4.a.a 224.a 1.a 11 13.21613.216 Q\Q None 224.4.a.a 00 2-2 00 77 ++ - SU(2)\mathrm{SU}(2) q2q3+7q723q9+20q1120q13+q-2q^{3}+7q^{7}-23q^{9}+20q^{11}-20q^{13}+\cdots
224.4.a.b 224.a 1.a 11 13.21613.216 Q\Q None 224.4.a.a 00 22 00 7-7 - ++ SU(2)\mathrm{SU}(2) q+2q37q723q920q1120q13+q+2q^{3}-7q^{7}-23q^{9}-20q^{11}-20q^{13}+\cdots
224.4.a.c 224.a 1.a 22 13.21613.216 Q(37)\Q(\sqrt{37}) None 224.4.a.c 00 6-6 6-6 1414 ++ - SU(2)\mathrm{SU}(2) q+(3β)q3+(3+β)q5+7q7+q+(-3-\beta )q^{3}+(-3+\beta )q^{5}+7q^{7}+\cdots
224.4.a.d 224.a 1.a 22 13.21613.216 Q(37)\Q(\sqrt{37}) None 224.4.a.c 00 66 6-6 14-14 ++ ++ SU(2)\mathrm{SU}(2) q+(3+β)q3+(3+β)q57q7+(19+)q9+q+(3+\beta )q^{3}+(-3+\beta )q^{5}-7q^{7}+(19+\cdots)q^{9}+\cdots
224.4.a.e 224.a 1.a 33 13.21613.216 3.3.2981.1 None 224.4.a.e 00 8-8 1010 21-21 ++ ++ SU(2)\mathrm{SU}(2) q+(3β1)q3+(3+β2)q57q7+q+(-3-\beta _{1})q^{3}+(3+\beta _{2})q^{5}-7q^{7}+\cdots
224.4.a.f 224.a 1.a 33 13.21613.216 3.3.621.1 None 224.4.a.f 00 00 6-6 21-21 - ++ SU(2)\mathrm{SU}(2) q+β1q3+(22β1β2)q57q7+q+\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}-7q^{7}+\cdots
224.4.a.g 224.a 1.a 33 13.21613.216 3.3.621.1 None 224.4.a.f 00 00 6-6 2121 - - SU(2)\mathrm{SU}(2) qβ1q3+(22β1β2)q5+7q7+q-\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}+7q^{7}+\cdots
224.4.a.h 224.a 1.a 33 13.21613.216 3.3.2981.1 None 224.4.a.e 00 88 1010 2121 - - SU(2)\mathrm{SU}(2) q+(3+β1)q3+(3+β2)q5+7q7+(11+)q9+q+(3+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+7q^{7}+(11+\cdots)q^{9}+\cdots

Decomposition of S4old(Γ0(224))S_{4}^{\mathrm{old}}(\Gamma_0(224)) into lower level spaces