Properties

Label 1170.2.a
Level 11701170
Weight 22
Character orbit 1170.a
Rep. character χ1170(1,)\chi_{1170}(1,\cdot)
Character field Q\Q
Dimension 2020
Newform subspaces 1717
Sturm bound 504504
Trace bound 1717

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Defining parameters

Level: N N == 1170=232513 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1170.a (trivial)
Character field: Q\Q
Newform subspaces: 17 17
Sturm bound: 504504
Trace bound: 1717
Distinguishing TpT_p: 77, 1111, 1717, 3131

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(1170))M_{2}(\Gamma_0(1170)).

Total New Old
Modular forms 268 20 248
Cusp forms 237 20 217
Eisenstein series 31 0 31

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

2233551313FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++++++13130013131212001212110011
++++++--19192217171717221515220022
++++-++-17171116161515111414220022
++++--++17171116161515111414220022
++-++++-18182216161616221414220022
++-++-++17172215151515221313220022
++--++++16162214141414221212220022
++----17171116161515111414220022
-++++++-18181117171616111515220022
-++++-++16161115151414111313220022
-++-++++18180018181616001616220022
-++---14142212121212221010220022
--++++++16161115151414111313220022
--++--17172215151515221313220022
---++-18182216161616221414220022
----++17170017171515001515220022
Plus space++13013077123123115115771081081515001515
Minus space-138138131312512512212213131091091616001616

Trace form

20q2q2+20q42q52q84q11+2q13+20q16+8q17+20q192q20+16q2216q23+20q25+16q298q312q324q34+8q35++14q98+O(q100) 20 q - 2 q^{2} + 20 q^{4} - 2 q^{5} - 2 q^{8} - 4 q^{11} + 2 q^{13} + 20 q^{16} + 8 q^{17} + 20 q^{19} - 2 q^{20} + 16 q^{22} - 16 q^{23} + 20 q^{25} + 16 q^{29} - 8 q^{31} - 2 q^{32} - 4 q^{34} + 8 q^{35}+ \cdots + 14 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(1170))S_{2}^{\mathrm{new}}(\Gamma_0(1170)) 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 5 13
1170.2.a.a 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.f 1-1 00 1-1 00 ++ - ++ - SU(2)\mathrm{SU}(2) qq2+q4q5q8+q104q11+q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots
1170.2.a.b 1170.a 1.a 11 9.3429.342 Q\Q None 130.2.a.b 1-1 00 1-1 00 ++ - ++ - SU(2)\mathrm{SU}(2) qq2+q4q5q8+q10+q13+q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{13}+\cdots
1170.2.a.c 1170.a 1.a 11 9.3429.342 Q\Q None 1170.2.a.c 1-1 00 11 4-4 ++ ++ - - SU(2)\mathrm{SU}(2) qq2+q4+q54q7q8q10+q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots
1170.2.a.d 1170.a 1.a 11 9.3429.342 Q\Q None 130.2.a.c 1-1 00 11 4-4 ++ - - ++ SU(2)\mathrm{SU}(2) qq2+q4+q54q7q8q10+q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots
1170.2.a.e 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.e 1-1 00 11 22 ++ - - ++ SU(2)\mathrm{SU}(2) qq2+q4+q5+2q7q8q10+q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots
1170.2.a.f 1170.a 1.a 11 9.3429.342 Q\Q None 1170.2.a.f 1-1 00 11 22 ++ ++ - ++ SU(2)\mathrm{SU}(2) qq2+q4+q5+2q7q8q10+q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots
1170.2.a.g 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.g 1-1 00 11 22 ++ - - - SU(2)\mathrm{SU}(2) qq2+q4+q5+2q7q8q10+q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots
1170.2.a.h 1170.a 1.a 11 9.3429.342 Q\Q None 1170.2.a.c 11 00 1-1 4-4 - ++ ++ - SU(2)\mathrm{SU}(2) q+q2+q4q54q7+q8q10+q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots
1170.2.a.i 1170.a 1.a 11 9.3429.342 Q\Q None 130.2.a.a 11 00 1-1 4-4 - - ++ - SU(2)\mathrm{SU}(2) q+q2+q4q54q7+q8q10+q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots
1170.2.a.j 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.b 11 00 1-1 2-2 - - ++ ++ SU(2)\mathrm{SU}(2) q+q2+q4q52q7+q8q10+q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots
1170.2.a.k 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.d 11 00 1-1 22 - - ++ - SU(2)\mathrm{SU}(2) q+q2+q4q5+2q7+q8q10+q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots
1170.2.a.l 1170.a 1.a 11 9.3429.342 Q\Q None 1170.2.a.f 11 00 1-1 22 - ++ ++ ++ SU(2)\mathrm{SU}(2) q+q2+q4q5+2q7+q8q10+q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots
1170.2.a.m 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.a 11 00 11 00 - - - ++ SU(2)\mathrm{SU}(2) q+q2+q4+q5+q8+q10q13+q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{13}+\cdots
1170.2.a.n 1170.a 1.a 11 9.3429.342 Q\Q None 390.2.a.c 11 00 11 44 - - - ++ SU(2)\mathrm{SU}(2) q+q2+q4+q5+4q7+q8+q10+q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots
1170.2.a.o 1170.a 1.a 22 9.3429.342 Q(2)\Q(\sqrt{2}) None 390.2.a.h 2-2 00 2-2 00 ++ - ++ ++ SU(2)\mathrm{SU}(2) qq2+q4q5+βq7q8+q10+q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots
1170.2.a.p 1170.a 1.a 22 9.3429.342 Q(13)\Q(\sqrt{13}) None 1170.2.a.p 2-2 00 2-2 22 ++ ++ ++ - SU(2)\mathrm{SU}(2) qq2+q4q5+(1+β)q7q8+q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots
1170.2.a.q 1170.a 1.a 22 9.3429.342 Q(13)\Q(\sqrt{13}) None 1170.2.a.p 22 00 22 22 - ++ - - SU(2)\mathrm{SU}(2) q+q2+q4+q5+(1+β)q7+q8+q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots

Decomposition of S2old(Γ0(1170))S_{2}^{\mathrm{old}}(\Gamma_0(1170)) into lower level spaces