Sato-Tate group data - 1.4.E.1.1a

Formats: - HTML - YAML - JSON - 2024-05-01T11:29:51.393186

• gps_st •

  Column	Type
  character_diagonal	bigint[]
  character_matrix	bigint[]
  component_group	text
  component_group_number	smallint
  components	smallint
  counts	jsonb
  degree	smallint
  first_a2_moment	smallint
  fourth_trace_moment	smallint
  gens	jsonb
  identity_component	text
  label	text
  label_components	integer[]
  maximal	boolean
  moments	jsonb
  name	text
  old_label	text
  pretty	text
  rational	boolean
  real_dimension	smallint
  second_trace_moment	smallint
  simplex	bigint[]
  st0_label	text
  subgroup_multiplicities	smallint[]
  subgroups	jsonb
  supgroup_multiplicities	smallint[]
  supgroups	jsonb
  trace_histogram	text
  trace_zero_density	text
  weight	smallint
  zvector	smallint[]

  
  {'character_diagonal': [1, 4, 5, 10, 20, 14, 20, 49, 56, 30], 'character_matrix': [[1, 0, 2, 1, 0, 3, 0, 2, 0, 4], [0, 4, 0, 0, 8, 0, 4, 0, 12, 0], [2, 0, 5, 5, 0, 8, 0, 10, 0, 11], [1, 0, 5, 10, 0, 9, 0, 20, 0, 13], [0, 8, 0, 0, 20, 0, 16, 0, 32, 0], [3, 0, 8, 9, 0, 14, 0, 21, 0, 20], [0, 4, 0, 0, 16, 0, 20, 0, 28, 0], [2, 0, 10, 20, 0, 21, 0, 49, 0, 32], [0, 12, 0, 0, 32, 0, 28, 0, 56, 0], [4, 0, 11, 13, 0, 20, 0, 32, 0, 30]], 'component_group': '1.1', 'component_group_number': 1, 'components': 1, 'counts': [], 'degree': 4, 'first_a2_moment': 3, 'fourth_trace_moment': 32, 'gens': [], 'identity_component': 'SU(2)_2', 'label': '1.4.E.1.1a', 'label_components': [1, 4, 4, 1, 1, 0], 'maximal': False, 'moments': [['a_1', 1, 0, 4, 0, 32, 0, 320, 0, 3584, 0, 43008, 0, 540672], ['a_2', 1, 3, 10, 37, 150, 654, 3012, 14445, 71398, 361114, 1859628, 9716194, 51373180]], 'name': 'E_1', 'old_label': '1.4.3.1.1a', 'pretty': 'E_1', 'rational': True, 'real_dimension': 3, 'second_trace_moment': 4, 'simplex': [3, 4, 10, 16, 32, 37, 68, 144, 320, 150, 304, 672, 1536, 3584, 654, 1416, 3232, 7552, 17920, 43008, 3012, 6816, 15936, 37888, 91136, 221184, 540672], 'st0_label': '1.4.E', 'subgroup_multiplicities': [], 'subgroups': [], 'supgroups': ['1.4.E.2.1a', '1.4.E.2.1b', '1.4.E.3.1a'], 'trace_histogram': 'data:image/png;base64,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', 'trace_zero_density': '0', 'weight': 1, 'zvector': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}
• gps_st0 •

  Column	Type
  degree	smallint
  description	text
  hodge_circle	text
  label	text
  label_components	integer[]
  name	text
  pretty	text
  real_dimension	smallint
  symplectic_form	text
  weight	smallint

  
  {'degree': 4, 'description': '\\left\\{\\begin{bmatrix}A&0\\\\0&\\bar{A}\\end{bmatrix}: A\\in \\mathrm{SU}(2)\\right\\}', 'hodge_circle': 'u\\mapsto\\mathrm{diag}(u,\\bar u,\\bar u,u)', 'label': '1.4.E', 'label_components': [1, 4, 4], 'name': 'SU(2)_2', 'pretty': '\\mathrm{SU}(2)_2', 'real_dimension': 3, 'symplectic_form': '\\begin{bmatrix}0&I_2\\\\-I_2&0\\end{bmatrix}', 'weight': 1}
• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_gens	numeric[]
  aut_group	text
  aut_order	numeric
  aut_stats	numeric[]
  cc_stats	numeric[]
  center_label	text
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  counter	integer
  cyclic	boolean
  derived_length	smallint
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  irrC_degree	integer
  irrQ_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_equivalence	boolean
  outer_group	text
  outer_order	numeric
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_gens': [], 'aut_group': '1.1', 'aut_order': 1, 'aut_stats': [[1, 1, 1, 1]], 'cc_stats': [[1, 1, 1]], 'center_label': '1.1', 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'irrC_degree': 1, 'irrQ_degree': 1, 'irrep_stats': [[1, 1]], 'label': '1.1', 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': None, 'normal_index_bound': None, 'normal_order_bound': None, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_equivalence': False, 'outer_group': '1.1', 'outer_order': 1, 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': []}, 'Perm': {'d': 1, 'gens': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}