Properties

Label 197.10.a
Level 197197
Weight 1010
Character orbit 197.a
Rep. character χ197(1,)\chi_{197}(1,\cdot)
Character field Q\Q
Dimension 147147
Newform subspaces 22
Sturm bound 165165
Trace bound 11

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Defining parameters

Level: N N == 197 197
Weight: k k == 10 10
Character orbit: [χ][\chi] == 197.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 165165
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M10(Γ0(197))M_{10}(\Gamma_0(197)).

Total New Old
Modular forms 149 147 2
Cusp forms 147 147 0
Eisenstein series 2 0 2

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

197197Dim
++7171
-7676

Trace form

147q+16q22q3+37632q4+2842q57584q6+1140q7+11574q8+938221q917814q1022610q1180896q12+46310q13+200706q14125252q15+9633792q16++2350789054q99+O(q100) 147 q + 16 q^{2} - 2 q^{3} + 37632 q^{4} + 2842 q^{5} - 7584 q^{6} + 1140 q^{7} + 11574 q^{8} + 938221 q^{9} - 17814 q^{10} - 22610 q^{11} - 80896 q^{12} + 46310 q^{13} + 200706 q^{14} - 125252 q^{15} + 9633792 q^{16}+ \cdots + 2350789054 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(Γ0(197))S_{10}^{\mathrm{new}}(\Gamma_0(197)) 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} 197
197.10.a.a 197.a 1.a 7171 101.462101.462 None 197.10.a.a 32-32 892-892 2329-2329 37846-37846 ++ SU(2)\mathrm{SU}(2)
197.10.a.b 197.a 1.a 7676 101.462101.462 None 197.10.a.b 4848 890890 51715171 3898638986 - SU(2)\mathrm{SU}(2)