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Degree Bad \(p\) Root analytic conductor Motivic weight Spectral label
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Columns to display Euler factor constraints
e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 11 }(T)\) \(F_{ 13 }(T)\) \(F_{ 17 }(T)\) \(F_{ 19 }(T)\) \(F_{ 23 }(T)\) \(F_{ 29 }(T)\) \(F_{ 31 }(T)\) \(F_{ 37 }(T)\) \(F_{ 41 }(T)\) \(F_{ 43 }(T)\) \(F_{ 47 }(T)\)
6-4536e3-1.1-c1e3-0-1 Modular form 4536.2.a.t $1$ $1$ $1 + 2 T^{3} + 125 T^{6}$ $( 1 - T )^{3}$ $1 + 3 T + 15 T^{2} + 30 T^{3} + 165 T^{4} + 363 T^{5} + 1331 T^{6}$ $1 + 6 T + 36 T^{2} + 132 T^{3} + 468 T^{4} + 1014 T^{5} + 2197 T^{6}$ $1 + 6 T + 42 T^{2} + 154 T^{3} + 714 T^{4} + 1734 T^{5} + 4913 T^{6}$ $1 + 33 T^{2} + 8 T^{3} + 627 T^{4} + 6859 T^{6}$ $1 + 6 T + 33 T^{2} + 68 T^{3} + 759 T^{4} + 3174 T^{5} + 12167 T^{6}$ $1 + 6 T + 42 T^{2} + 86 T^{3} + 1218 T^{4} + 5046 T^{5} + 24389 T^{6}$ $1 + 69 T^{2} + 8 T^{3} + 2139 T^{4} + 29791 T^{6}$ $1 + 15 T + 162 T^{2} + 1107 T^{3} + 5994 T^{4} + 20535 T^{5} + 50653 T^{6}$ $( 1 - 2 T + 41 T^{2} )^{3}$ $1 - 3 T + 9 T^{2} + 142 T^{3} + 387 T^{4} - 5547 T^{5} + 79507 T^{6}$ $1 - 6 T - 15 T^{2} + 572 T^{3} - 705 T^{4} - 13254 T^{5} + 103823 T^{6}$
6-9072e3-1.1-c1e3-0-7 Modular form 9072.2.a.bw $1$ $1$ $1 - 2 T^{3} + 125 T^{6}$ $( 1 + T )^{3}$ $1 + 3 T + 15 T^{2} + 30 T^{3} + 165 T^{4} + 363 T^{5} + 1331 T^{6}$ $1 + 6 T + 36 T^{2} + 132 T^{3} + 468 T^{4} + 1014 T^{5} + 2197 T^{6}$ $1 - 6 T + 42 T^{2} - 154 T^{3} + 714 T^{4} - 1734 T^{5} + 4913 T^{6}$ $1 + 33 T^{2} - 8 T^{3} + 627 T^{4} + 6859 T^{6}$ $1 + 6 T + 33 T^{2} + 68 T^{3} + 759 T^{4} + 3174 T^{5} + 12167 T^{6}$ $1 - 6 T + 42 T^{2} - 86 T^{3} + 1218 T^{4} - 5046 T^{5} + 24389 T^{6}$ $1 + 69 T^{2} - 8 T^{3} + 2139 T^{4} + 29791 T^{6}$ $1 + 15 T + 162 T^{2} + 1107 T^{3} + 5994 T^{4} + 20535 T^{5} + 50653 T^{6}$ $( 1 + 2 T + 41 T^{2} )^{3}$ $1 + 3 T + 9 T^{2} - 142 T^{3} + 387 T^{4} + 5547 T^{5} + 79507 T^{6}$ $1 - 6 T - 15 T^{2} + 572 T^{3} - 705 T^{4} - 13254 T^{5} + 103823 T^{6}$