Properties

Label 91.2.c
Level 91
Weight 2
Character orbit c
Rep. character \(\chi_{91}(64,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 91 = 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 91.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q - 4q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{9} - 20q^{12} + 8q^{13} - 4q^{14} + 8q^{16} - 8q^{17} + 24q^{22} + 6q^{23} + 8q^{25} + 12q^{26} - 12q^{27} - 14q^{29} + 16q^{30} - 6q^{35} + 4q^{36} - 4q^{38} - 8q^{39} - 20q^{40} - 4q^{42} - 26q^{43} + 8q^{48} - 6q^{49} + 8q^{51} - 20q^{52} + 2q^{53} + 12q^{55} + 12q^{56} + 28q^{61} + 16q^{62} - 8q^{64} - 6q^{65} + 28q^{66} + 20q^{68} - 4q^{69} - 24q^{74} + 44q^{75} + 16q^{77} + 16q^{78} + 26q^{79} - 26q^{81} - 56q^{82} - 40q^{87} - 40q^{88} - 12q^{90} - 2q^{91} - 36q^{92} + 20q^{94} + 58q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
91.2.c.a \(6\) \(0.727\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 4 T^{2} + 8 T^{4} - 12 T^{6} + 32 T^{8} - 64 T^{10} + 64 T^{12} \)
$3$ \( ( 1 + 5 T^{2} + 2 T^{3} + 15 T^{4} + 27 T^{6} )^{2} \)
$5$ \( 1 - 19 T^{2} + 162 T^{4} - 919 T^{6} + 4050 T^{8} - 11875 T^{10} + 15625 T^{12} \)
$7$ \( ( 1 + T^{2} )^{3} \)
$11$ \( 1 - 38 T^{2} + 747 T^{4} - 9800 T^{6} + 90387 T^{8} - 556358 T^{10} + 1771561 T^{12} \)
$13$ \( 1 - 8 T + 7 T^{2} + 64 T^{3} + 91 T^{4} - 1352 T^{5} + 2197 T^{6} \)
$17$ \( ( 1 + 4 T + 43 T^{2} + 102 T^{3} + 731 T^{4} + 1156 T^{5} + 4913 T^{6} )^{2} \)
$19$ \( 1 + 5 T^{2} + 238 T^{4} + 10877 T^{6} + 85918 T^{8} + 651605 T^{10} + 47045881 T^{12} \)
$23$ \( ( 1 - 3 T + 44 T^{2} - 59 T^{3} + 1012 T^{4} - 1587 T^{5} + 12167 T^{6} )^{2} \)
$29$ \( ( 1 + 7 T + 66 T^{2} + 411 T^{3} + 1914 T^{4} + 5887 T^{5} + 24389 T^{6} )^{2} \)
$31$ \( 1 - 103 T^{2} + 5914 T^{4} - 224059 T^{6} + 5683354 T^{8} - 95122663 T^{10} + 887503681 T^{12} \)
$37$ \( 1 - 114 T^{2} + 6171 T^{4} - 242912 T^{6} + 8448099 T^{8} - 213654354 T^{10} + 2565726409 T^{12} \)
$41$ \( 1 - 138 T^{2} + 10367 T^{4} - 522380 T^{6} + 17426927 T^{8} - 389955018 T^{10} + 4750104241 T^{12} \)
$43$ \( ( 1 + 13 T + 164 T^{2} + 1101 T^{3} + 7052 T^{4} + 24037 T^{5} + 79507 T^{6} )^{2} \)
$47$ \( 1 - 131 T^{2} + 10566 T^{4} - 603323 T^{6} + 23340294 T^{8} - 639238211 T^{10} + 10779215329 T^{12} \)
$53$ \( ( 1 - T + 150 T^{2} - 93 T^{3} + 7950 T^{4} - 2809 T^{5} + 148877 T^{6} )^{2} \)
$59$ \( 1 - 286 T^{2} + 36983 T^{4} - 2780916 T^{6} + 128737823 T^{8} - 3465565246 T^{10} + 42180533641 T^{12} \)
$61$ \( ( 1 - 14 T + 211 T^{2} - 1556 T^{3} + 12871 T^{4} - 52094 T^{5} + 226981 T^{6} )^{2} \)
$67$ \( 1 - 322 T^{2} + 47303 T^{4} - 4048956 T^{6} + 212343167 T^{8} - 6488660962 T^{10} + 90458382169 T^{12} \)
$71$ \( 1 - 122 T^{2} + 17115 T^{4} - 1124048 T^{6} + 86276715 T^{8} - 3100225082 T^{10} + 128100283921 T^{12} \)
$73$ \( 1 - 175 T^{2} + 10862 T^{4} - 497775 T^{6} + 57883598 T^{8} - 4969692175 T^{10} + 151334226289 T^{12} \)
$79$ \( ( 1 - 13 T + 200 T^{2} - 1869 T^{3} + 15800 T^{4} - 81133 T^{5} + 493039 T^{6} )^{2} \)
$83$ \( 1 - 271 T^{2} + 41066 T^{4} - 4200123 T^{6} + 282903674 T^{8} - 12861204991 T^{10} + 326940373369 T^{12} \)
$89$ \( 1 - 415 T^{2} + 80838 T^{4} - 9173143 T^{6} + 640317798 T^{8} - 26038030015 T^{10} + 496981290961 T^{12} \)
$97$ \( 1 - 7 T^{2} + 14150 T^{4} + 326769 T^{6} + 133137350 T^{8} - 619704967 T^{10} + 832972004929 T^{12} \)
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