Properties

Label 134.2.a
Level 134
Weight 2
Character orbit a
Rep. character \(\chi_{134}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 2
Sturm bound 34
Trace bound 2

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Defining parameters

Level: \( N \) = \( 134 = 2 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 134.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(34\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(134))\).

Total New Old
Modular forms 19 6 13
Cusp forms 16 6 10
Eisenstein series 3 0 3

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

\(2\)\(67\)FrickeDim.
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(6\)

Trace form

\( 6q + 4q^{3} + 6q^{4} + 2q^{6} + 8q^{9} + O(q^{10}) \) \( 6q + 4q^{3} + 6q^{4} + 2q^{6} + 8q^{9} - 6q^{10} - 4q^{11} + 4q^{12} + 8q^{13} - 8q^{15} + 6q^{16} - 6q^{17} - 8q^{18} + 12q^{19} - 12q^{21} - 2q^{22} - 14q^{23} + 2q^{24} + 4q^{25} - 14q^{26} - 8q^{27} - 12q^{29} - 16q^{30} + 16q^{31} - 32q^{33} - 20q^{35} + 8q^{36} + 4q^{37} - 16q^{39} - 6q^{40} - 4q^{41} + 4q^{43} - 4q^{44} - 12q^{45} + 8q^{46} + 22q^{47} + 4q^{48} + 22q^{49} + 8q^{50} + 8q^{51} + 8q^{52} - 12q^{53} + 20q^{54} + 16q^{55} + 20q^{57} - 12q^{58} - 8q^{60} + 36q^{61} + 8q^{62} - 20q^{63} + 6q^{64} + 12q^{65} + 8q^{66} - 6q^{68} + 16q^{69} + 20q^{70} + 14q^{71} - 8q^{72} - 14q^{73} - 4q^{74} + 64q^{75} + 12q^{76} + 8q^{77} + 4q^{78} + 4q^{79} + 6q^{81} + 4q^{82} - 4q^{83} - 12q^{84} - 28q^{85} + 2q^{86} - 12q^{87} - 2q^{88} + 22q^{89} - 42q^{90} + 16q^{91} - 14q^{92} - 20q^{93} + 20q^{94} + 2q^{96} + 16q^{97} - 16q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(134))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 67
134.2.a.a \(3\) \(1.070\) 3.3.473.1 None \(-3\) \(1\) \(3\) \(0\) \(+\) \(-\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
134.2.a.b \(3\) \(1.070\) \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(134))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(134)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))
$3$ (\( 1 - T + T^{2} + 5 T^{3} + 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 - 3 T + 9 T^{2} - 17 T^{3} + 27 T^{4} - 27 T^{5} + 27 T^{6} \))
$5$ (\( 1 - 3 T + 13 T^{2} - 27 T^{3} + 65 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 + 3 T + 9 T^{2} + 31 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6} \))
$7$ (\( 1 + T^{2} + 8 T^{3} + 7 T^{4} + 343 T^{6} \))(\( 1 + 9 T^{2} - 8 T^{3} + 63 T^{4} + 343 T^{6} \))
$11$ (\( 1 + T + 17 T^{2} + 31 T^{3} + 187 T^{4} + 121 T^{5} + 1331 T^{6} \))(\( 1 + 3 T + 9 T^{2} + 13 T^{3} + 99 T^{4} + 363 T^{5} + 1331 T^{6} \))
$13$ (\( 1 - 11 T + 69 T^{2} - 295 T^{3} + 897 T^{4} - 1859 T^{5} + 2197 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 75 T^{3} + 273 T^{4} + 507 T^{5} + 2197 T^{6} \))
$17$ (\( 1 + 3 T + 49 T^{2} + 99 T^{3} + 833 T^{4} + 867 T^{5} + 4913 T^{6} \))(\( 1 + 3 T + 33 T^{2} + 99 T^{3} + 561 T^{4} + 867 T^{5} + 4913 T^{6} \))
$19$ (\( ( 1 - 2 T + 19 T^{2} )^{3} \))(\( 1 - 6 T + 21 T^{2} - 76 T^{3} + 399 T^{4} - 2166 T^{5} + 6859 T^{6} \))
$23$ (\( 1 + 11 T + 101 T^{2} + 533 T^{3} + 2323 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + 3 T + 33 T^{2} + 189 T^{3} + 759 T^{4} + 1587 T^{5} + 12167 T^{6} \))
$29$ (\( ( 1 + 29 T^{2} )^{3} \))(\( ( 1 + 4 T + 29 T^{2} )^{3} \))
$31$ (\( 1 - 4 T + 9 T^{2} + 192 T^{3} + 279 T^{4} - 3844 T^{5} + 29791 T^{6} \))(\( 1 - 12 T + 129 T^{2} - 752 T^{3} + 3999 T^{4} - 11532 T^{5} + 29791 T^{6} \))
$37$ (\( 1 - 4 T + 51 T^{2} - 96 T^{3} + 1887 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 + 27 T^{2} - 136 T^{3} + 999 T^{4} + 50653 T^{6} \))
$41$ (\( 1 + 4 T - T^{2} - 272 T^{3} - 41 T^{4} + 6724 T^{5} + 68921 T^{6} \))(\( 1 + 111 T^{2} - 8 T^{3} + 4551 T^{4} + 68921 T^{6} \))
$43$ (\( 1 - T + 69 T^{2} + 81 T^{3} + 2967 T^{4} - 1849 T^{5} + 79507 T^{6} \))(\( 1 - 3 T + 69 T^{2} - 205 T^{3} + 2967 T^{4} - 5547 T^{5} + 79507 T^{6} \))
$47$ (\( 1 - T + 125 T^{2} - 103 T^{3} + 5875 T^{4} - 2209 T^{5} + 103823 T^{6} \))(\( 1 - 21 T + 285 T^{2} - 2295 T^{3} + 13395 T^{4} - 46389 T^{5} + 103823 T^{6} \))
$53$ (\( 1 + 3 T + 85 T^{2} + 363 T^{3} + 4505 T^{4} + 8427 T^{5} + 148877 T^{6} \))(\( 1 + 9 T + 177 T^{2} + 945 T^{3} + 9381 T^{4} + 25281 T^{5} + 148877 T^{6} \))
$59$ (\( 1 - 3 T^{2} + 216 T^{3} - 177 T^{4} + 205379 T^{6} \))(\( 1 + 165 T^{2} + 8 T^{3} + 9735 T^{4} + 205379 T^{6} \))
$61$ (\( 1 - 21 T + 253 T^{2} - 2245 T^{3} + 15433 T^{4} - 78141 T^{5} + 226981 T^{6} \))(\( 1 - 15 T + 249 T^{2} - 1919 T^{3} + 15189 T^{4} - 55815 T^{5} + 226981 T^{6} \))
$67$ (\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))
$71$ (\( 1 - 5 T + 125 T^{2} - 875 T^{3} + 8875 T^{4} - 25205 T^{5} + 357911 T^{6} \))(\( 1 - 9 T + 201 T^{2} - 1099 T^{3} + 14271 T^{4} - 45369 T^{5} + 357911 T^{6} \))
$73$ (\( 1 + 23 T + 333 T^{2} + 3147 T^{3} + 24309 T^{4} + 122567 T^{5} + 389017 T^{6} \))(\( 1 - 9 T + 165 T^{2} - 1341 T^{3} + 12045 T^{4} - 47961 T^{5} + 389017 T^{6} \))
$79$ (\( 1 - 10 T + 141 T^{2} - 756 T^{3} + 11139 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 6 T + 213 T^{2} + 956 T^{3} + 16827 T^{4} + 37446 T^{5} + 493039 T^{6} \))
$83$ (\( 1 + 22 T + 281 T^{2} + 2668 T^{3} + 23323 T^{4} + 151558 T^{5} + 571787 T^{6} \))(\( 1 - 18 T + 249 T^{2} - 2340 T^{3} + 20667 T^{4} - 124002 T^{5} + 571787 T^{6} \))
$89$ (\( 1 - 19 T + 365 T^{2} - 3535 T^{3} + 32485 T^{4} - 150499 T^{5} + 704969 T^{6} \))(\( 1 - 3 T + 141 T^{2} - 855 T^{3} + 12549 T^{4} - 23763 T^{5} + 704969 T^{6} \))
$97$ (\( 1 + 2 T + 155 T^{2} + 908 T^{3} + 15035 T^{4} + 18818 T^{5} + 912673 T^{6} \))(\( 1 - 18 T + 315 T^{2} - 2908 T^{3} + 30555 T^{4} - 169362 T^{5} + 912673 T^{6} \))
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