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Properties

Label 108.3.g
Level 108
Weight 3
Character orbit g
Rep. character \(\chi_{108}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 54
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

Total New Old
Modular forms 90 4 86
Cusp forms 54 4 50
Eisenstein series 36 0 36

Trace form

\( 4q - 9q^{5} - q^{7} + O(q^{10}) \) \( 4q - 9q^{5} - q^{7} + 36q^{11} + 5q^{13} + 2q^{19} - 99q^{23} + 13q^{25} + 63q^{29} - 7q^{31} - 64q^{37} + 18q^{41} - 46q^{43} + 81q^{47} - 51q^{49} + 90q^{55} - 126q^{59} + 41q^{61} - 171q^{65} + 116q^{67} + 86q^{73} + 279q^{77} + 83q^{79} + 81q^{83} + 18q^{85} - 302q^{91} + 144q^{95} - 196q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.3.g.a \(4\) \(2.943\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-9\) \(-1\) \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 + 9 T + 59 T^{2} + 288 T^{3} + 1074 T^{4} + 7200 T^{5} + 36875 T^{6} + 140625 T^{7} + 390625 T^{8} \)
$7$ \( 1 + T - 23 T^{2} - 74 T^{3} - 1874 T^{4} - 3626 T^{5} - 55223 T^{6} + 117649 T^{7} + 5764801 T^{8} \)
$11$ \( 1 - 36 T + 683 T^{2} - 9036 T^{3} + 100632 T^{4} - 1093356 T^{5} + 9999803 T^{6} - 63776196 T^{7} + 214358881 T^{8} \)
$13$ \( 1 - 5 T - 245 T^{2} + 340 T^{3} + 40114 T^{4} + 57460 T^{5} - 6997445 T^{6} - 24134045 T^{7} + 815730721 T^{8} \)
$17$ \( 1 - 769 T^{2} + 298176 T^{4} - 64227649 T^{6} + 6975757441 T^{8} \)
$19$ \( ( 1 - T + 648 T^{2} - 361 T^{3} + 130321 T^{4} )^{2} \)
$23$ \( 1 + 99 T + 5117 T^{2} + 183150 T^{3} + 4870902 T^{4} + 96886350 T^{5} + 1431946397 T^{6} + 14655553011 T^{7} + 78310985281 T^{8} \)
$29$ \( 1 - 63 T + 2123 T^{2} - 50400 T^{3} + 1045362 T^{4} - 42386400 T^{5} + 1501557563 T^{6} - 37473869223 T^{7} + 500246412961 T^{8} \)
$31$ \( 1 + 7 T - 1217 T^{2} - 4592 T^{3} + 632146 T^{4} - 4412912 T^{5} - 1123925057 T^{6} + 6212525767 T^{7} + 852891037441 T^{8} \)
$37$ \( ( 1 + 32 T + 1806 T^{2} + 43808 T^{3} + 1874161 T^{4} )^{2} \)
$41$ \( 1 - 18 T + 1913 T^{2} - 32490 T^{3} + 613812 T^{4} - 54615690 T^{5} + 5405680793 T^{6} - 85501876338 T^{7} + 7984925229121 T^{8} \)
$43$ \( ( 1 + 23 T - 1320 T^{2} + 42527 T^{3} + 3418801 T^{4} )^{2} \)
$47$ \( 1 - 81 T + 6929 T^{2} - 384102 T^{3} + 22437966 T^{4} - 848481318 T^{5} + 33811309649 T^{6} - 873116441649 T^{7} + 23811286661761 T^{8} \)
$53$ \( 1 - 7204 T^{2} + 26018214 T^{4} - 56843025124 T^{6} + 62259690411361 T^{8} \)
$59$ \( 1 + 126 T + 11993 T^{2} + 844326 T^{3} + 51207492 T^{4} + 2939098806 T^{5} + 145323510473 T^{6} + 5314747238766 T^{7} + 146830437604321 T^{8} \)
$61$ \( 1 - 41 T - 5513 T^{2} + 10168 T^{3} + 31652794 T^{4} + 37835128 T^{5} - 76332121433 T^{6} - 2112335348801 T^{7} + 191707312997281 T^{8} \)
$67$ \( 1 - 116 T + 3787 T^{2} - 80156 T^{3} + 12934456 T^{4} - 359820284 T^{5} + 76312295227 T^{6} - 10493172331604 T^{7} + 406067677556641 T^{8} \)
$71$ \( 1 - 18616 T^{2} + 137194926 T^{4} - 473063853496 T^{6} + 645753531245761 T^{8} \)
$73$ \( ( 1 - 43 T + 10452 T^{2} - 229147 T^{3} + 28398241 T^{4} )^{2} \)
$79$ \( 1 - 83 T - 5459 T^{2} + 11122 T^{3} + 70528774 T^{4} + 69412402 T^{5} - 212628492179 T^{6} - 20176258808243 T^{7} + 1517108809906561 T^{8} \)
$83$ \( 1 - 81 T + 16289 T^{2} - 1142262 T^{3} + 166474326 T^{4} - 7869042918 T^{5} + 773048590769 T^{6} - 26482170242889 T^{7} + 2252292232139041 T^{8} \)
$89$ \( 1 - 6916 T^{2} + 69013446 T^{4} - 433925338756 T^{6} + 3936588805702081 T^{8} \)
$97$ \( 1 + 196 T + 10291 T^{2} + 1824172 T^{3} + 341030200 T^{4} + 17163634348 T^{5} + 911054830771 T^{6} + 163262512966084 T^{7} + 7837433594376961 T^{8} \)
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