Properties

Label 2106.2.a
Level 21062106
Weight 22
Character orbit 2106.a
Rep. character χ2106(1,)\chi_{2106}(1,\cdot)
Character field Q\Q
Dimension 4848
Newform subspaces 2222
Sturm bound 756756
Trace bound 1111

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Defining parameters

Level: N N == 2106=23413 2106 = 2 \cdot 3^{4} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2106.a (trivial)
Character field: Q\Q
Newform subspaces: 22 22
Sturm bound: 756756
Trace bound: 1111
Distinguishing TpT_p: 55, 77, 1111

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(2106))M_{2}(\Gamma_0(2106)).

Total New Old
Modular forms 402 48 354
Cusp forms 355 48 307
Eisenstein series 47 0 47

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

22331313FrickeDim
++++++++66
++++--77
++-++-66
++--++55
-++++-88
-++-++33
--++++44
----99
Plus space++1818
Minus space-3030

Trace form

48q+48q4+48q16+12q19+12q22+72q25+24q31+12q34+24q3736q43+24q46+24q49+24q58+24q61+48q64+36q67+48q7036q73++36q97+O(q100) 48 q + 48 q^{4} + 48 q^{16} + 12 q^{19} + 12 q^{22} + 72 q^{25} + 24 q^{31} + 12 q^{34} + 24 q^{37} - 36 q^{43} + 24 q^{46} + 24 q^{49} + 24 q^{58} + 24 q^{61} + 48 q^{64} + 36 q^{67} + 48 q^{70} - 36 q^{73}+ \cdots + 36 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(2106))S_{2}^{\mathrm{new}}(\Gamma_0(2106)) 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 3 13
2106.2.a.a 2106.a 1.a 11 16.81616.816 Q\Q None 2106.2.a.a 1-1 00 00 1-1 ++ ++ - SU(2)\mathrm{SU}(2) qq2+q4q7q8+3q11+q13+q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots
2106.2.a.b 2106.a 1.a 11 16.81616.816 Q\Q None 234.2.e.a 1-1 00 22 2-2 ++ - - SU(2)\mathrm{SU}(2) qq2+q4+2q52q7q82q10+q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots
2106.2.a.c 2106.a 1.a 11 16.81616.816 Q\Q None 2106.2.a.c 1-1 00 22 11 ++ ++ - SU(2)\mathrm{SU}(2) qq2+q4+2q5+q7q82q10+q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots
2106.2.a.d 2106.a 1.a 11 16.81616.816 Q\Q None 234.2.e.a 11 00 2-2 2-2 - ++ - SU(2)\mathrm{SU}(2) q+q2+q42q52q7+q82q10+q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots
2106.2.a.e 2106.a 1.a 11 16.81616.816 Q\Q None 2106.2.a.c 11 00 2-2 11 - ++ - SU(2)\mathrm{SU}(2) q+q2+q42q5+q7+q82q10+q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots
2106.2.a.f 2106.a 1.a 11 16.81616.816 Q\Q None 2106.2.a.a 11 00 00 1-1 - ++ - SU(2)\mathrm{SU}(2) q+q2+q4q7+q83q11+q13+q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots
2106.2.a.g 2106.a 1.a 22 16.81616.816 Q(6)\Q(\sqrt{6}) None 2106.2.a.g 2-2 00 4-4 22 ++ ++ ++ SU(2)\mathrm{SU}(2) qq2+q4+(2+β)q5+q7q8+q-q^{2}+q^{4}+(-2+\beta )q^{5}+q^{7}-q^{8}+\cdots
2106.2.a.h 2106.a 1.a 22 16.81616.816 Q(6)\Q(\sqrt{6}) None 234.2.e.c 2-2 00 00 44 ++ ++ - SU(2)\mathrm{SU}(2) qq2+q4+βq5+2q7q8βq10+q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots
2106.2.a.i 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 234.2.e.b 2-2 00 22 4-4 ++ ++ ++ SU(2)\mathrm{SU}(2) qq2+q4+(1+β)q52q7q8+q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots
2106.2.a.j 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 2106.2.a.j 2-2 00 22 4-4 ++ - ++ SU(2)\mathrm{SU}(2) qq2+q4+(1+β)q5+(2+β)q7+q-q^{2}+q^{4}+(1+\beta )q^{5}+(-2+\beta )q^{7}+\cdots
2106.2.a.k 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 2106.2.a.k 2-2 00 22 22 ++ ++ ++ SU(2)\mathrm{SU}(2) qq2+q4+(1+β)q5+(12β)q7+q-q^{2}+q^{4}+(1+\beta )q^{5}+(1-2\beta )q^{7}+\cdots
2106.2.a.l 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 2106.2.a.j 22 00 2-2 4-4 - - ++ SU(2)\mathrm{SU}(2) q+q2+q4+(1+β)q5+(2β)q7+q+q^{2}+q^{4}+(-1+\beta )q^{5}+(-2-\beta )q^{7}+\cdots
2106.2.a.m 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 234.2.e.b 22 00 2-2 4-4 - - ++ SU(2)\mathrm{SU}(2) q+q2+q4+(1+β)q52q7+q8+q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots
2106.2.a.n 2106.a 1.a 22 16.81616.816 Q(3)\Q(\sqrt{3}) None 2106.2.a.k 22 00 2-2 22 - ++ ++ SU(2)\mathrm{SU}(2) q+q2+q4+(1+β)q5+(1+2β)q7+q+q^{2}+q^{4}+(-1+\beta )q^{5}+(1+2\beta )q^{7}+\cdots
2106.2.a.o 2106.a 1.a 22 16.81616.816 Q(6)\Q(\sqrt{6}) None 234.2.e.c 22 00 00 44 - - - SU(2)\mathrm{SU}(2) q+q2+q4+βq5+2q7+q8+βq10+q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots
2106.2.a.p 2106.a 1.a 22 16.81616.816 Q(6)\Q(\sqrt{6}) None 2106.2.a.g 22 00 44 22 - ++ ++ SU(2)\mathrm{SU}(2) q+q2+q4+(2+β)q5+q7+q8+q+q^{2}+q^{4}+(2+\beta )q^{5}+q^{7}+q^{8}+\cdots
2106.2.a.q 2106.a 1.a 33 16.81616.816 3.3.321.1 None 234.2.e.d 3-3 00 2-2 2-2 ++ ++ - SU(2)\mathrm{SU}(2) qq2+q4+(β1+β2)q5+(1+)q7+q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots
2106.2.a.r 2106.a 1.a 33 16.81616.816 3.3.321.1 None 234.2.e.d 33 00 22 2-2 - - - SU(2)\mathrm{SU}(2) q+q2+q4+(β1β2)q5+(1+2β1+)q7+q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots
2106.2.a.s 2106.a 1.a 44 16.81616.816 Q(3,7)\Q(\sqrt{3}, \sqrt{7}) None 2106.2.a.s 4-4 00 2-2 00 ++ - - SU(2)\mathrm{SU}(2) qq2+q4+(1+β1β2)q5+(β1+)q7+q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots
2106.2.a.t 2106.a 1.a 44 16.81616.816 4.4.22545.1 None 234.2.e.e 4-4 00 2-2 44 ++ - ++ SU(2)\mathrm{SU}(2) qq2+q4+β1q5+(1+β3)q7q8+q-q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots
2106.2.a.u 2106.a 1.a 44 16.81616.816 Q(3,7)\Q(\sqrt{3}, \sqrt{7}) None 2106.2.a.s 44 00 22 00 - - - SU(2)\mathrm{SU}(2) q+q2+q4+(1β1+β2)q5+(β1+)q7+q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots
2106.2.a.v 2106.a 1.a 44 16.81616.816 4.4.22545.1 None 234.2.e.e 44 00 22 44 - ++ ++ SU(2)\mathrm{SU}(2) q+q2+q4β1q5+(1+β3)q7+q8+q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}+q^{8}+\cdots

Decomposition of S2old(Γ0(2106))S_{2}^{\mathrm{old}}(\Gamma_0(2106)) into lower level spaces