Properties

Label 197.14.a
Level 197197
Weight 1414
Character orbit 197.a
Rep. character χ197(1,)\chi_{197}(1,\cdot)
Character field Q\Q
Dimension 213213
Newform subspaces 22
Sturm bound 231231
Trace bound 11

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Defining parameters

Level: N N == 197 197
Weight: k k == 14 14
Character orbit: [χ][\chi] == 197.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 231231
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M14(Γ0(197))M_{14}(\Gamma_0(197)).

Total New Old
Modular forms 215 213 2
Cusp forms 213 213 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
++104104
-109109

Trace form

213q+64q22q3+880640q410508q5+299904q6403306q7290442q8+111071167q9+6747306q10+10510498q114931584q1235067412q1314577374q14++3417936671410q99+O(q100) 213 q + 64 q^{2} - 2 q^{3} + 880640 q^{4} - 10508 q^{5} + 299904 q^{6} - 403306 q^{7} - 290442 q^{8} + 111071167 q^{9} + 6747306 q^{10} + 10510498 q^{11} - 4931584 q^{12} - 35067412 q^{13} - 14577374 q^{14}+ \cdots + 3417936671410 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S14new(Γ0(197))S_{14}^{\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
197.14.a.a 197.a 1.a 104104 211.245211.245 None 197.14.a.a 128-128 8020-8020 99004-99004 2084037-2084037 ++ SU(2)\mathrm{SU}(2)
197.14.a.b 197.a 1.a 109109 211.245211.245 None 197.14.a.b 192192 80188018 8849688496 16807311680731 - SU(2)\mathrm{SU}(2)