Properties

Label 108.5.c
Level 108
Weight 5
Character orbit c
Rep. character \(\chi_{108}(53,\cdot)\)
Character field \(\Q\)
Dimension 5
Newform subspaces 3
Sturm bound 90
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(90\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(108, [\chi])\).

Total New Old
Modular forms 81 5 76
Cusp forms 63 5 58
Eisenstein series 18 0 18

Trace form

\( 5q - 29q^{7} + O(q^{10}) \) \( 5q - 29q^{7} - 359q^{13} - 23q^{19} - 925q^{25} - 2756q^{31} + 3253q^{37} + 1426q^{43} - 9504q^{49} + 17334q^{55} + 2293q^{61} - 8027q^{67} + 15151q^{73} + 3301q^{79} - 27540q^{85} + 18995q^{91} - 1037q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.5.c.a \(1\) \(11.164\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(23\) \(q+23q^{7}+191q^{13}+647q^{19}+5^{4}q^{25}+\cdots\)
108.5.c.b \(2\) \(11.164\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-62\) \(q+\beta q^{5}-31q^{7}-5\beta q^{11}-241q^{13}+\cdots\)
108.5.c.c \(2\) \(11.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) \(q+iq^{5}+5q^{7}+13iq^{11}-34q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 25 T )( 1 + 25 T ) \))(\( 1 + 694 T^{2} + 390625 T^{4} \))(\( 1 - 1169 T^{2} + 390625 T^{4} \))
$7$ (\( 1 - 23 T + 2401 T^{2} \))(\( ( 1 + 31 T + 2401 T^{2} )^{2} \))(\( ( 1 - 5 T + 2401 T^{2} )^{2} \))
$11$ (\( ( 1 - 121 T )( 1 + 121 T ) \))(\( 1 + 19318 T^{2} + 214358881 T^{4} \))(\( 1 - 15593 T^{2} + 214358881 T^{4} \))
$13$ (\( 1 - 191 T + 28561 T^{2} \))(\( ( 1 + 241 T + 28561 T^{2} )^{2} \))(\( ( 1 + 34 T + 28561 T^{2} )^{2} \))
$17$ (\( ( 1 - 289 T )( 1 + 289 T ) \))(\( 1 - 118442 T^{2} + 6975757441 T^{4} \))(\( 1 + 35458 T^{2} + 6975757441 T^{4} \))
$19$ (\( 1 - 647 T + 130321 T^{2} \))(\( ( 1 + 271 T + 130321 T^{2} )^{2} \))(\( ( 1 + 64 T + 130321 T^{2} )^{2} \))
$23$ (\( ( 1 - 529 T )( 1 + 529 T ) \))(\( 1 - 511082 T^{2} + 78310985281 T^{4} \))(\( 1 - 185138 T^{2} + 78310985281 T^{4} \))
$29$ (\( ( 1 - 841 T )( 1 + 841 T ) \))(\( 1 - 1220162 T^{2} + 500246412961 T^{4} \))(\( 1 - 286718 T^{2} + 500246412961 T^{4} \))
$31$ (\( 1 - 194 T + 923521 T^{2} \))(\( ( 1 + 778 T + 923521 T^{2} )^{2} \))(\( ( 1 + 697 T + 923521 T^{2} )^{2} \))
$37$ (\( 1 - 2591 T + 1874161 T^{2} \))(\( ( 1 - 1079 T + 1874161 T^{2} )^{2} \))(\( ( 1 + 748 T + 1874161 T^{2} )^{2} \))
$41$ (\( ( 1 - 1681 T )( 1 + 1681 T ) \))(\( 1 - 791522 T^{2} + 7984925229121 T^{4} \))(\( 1 - 5183666 T^{2} + 7984925229121 T^{4} \))
$43$ (\( 1 + 3214 T + 3418801 T^{2} \))(\( ( 1 + 298 T + 3418801 T^{2} )^{2} \))(\( ( 1 - 2618 T + 3418801 T^{2} )^{2} \))
$47$ (\( ( 1 - 2209 T )( 1 + 2209 T ) \))(\( 1 + 1175638 T^{2} + 23811286661761 T^{4} \))(\( 1 - 2758046 T^{2} + 23811286661761 T^{4} \))
$53$ (\( ( 1 - 2809 T )( 1 + 2809 T ) \))(\( 1 - 6255362 T^{2} + 62259690411361 T^{4} \))(\( 1 - 14633921 T^{2} + 62259690411361 T^{4} \))
$59$ (\( ( 1 - 3481 T )( 1 + 3481 T ) \))(\( 1 - 16021322 T^{2} + 146830437604321 T^{4} \))(\( 1 + 9567874 T^{2} + 146830437604321 T^{4} \))
$61$ (\( 1 + 5233 T + 13845841 T^{2} \))(\( ( 1 + 2641 T + 13845841 T^{2} )^{2} \))(\( ( 1 - 6404 T + 13845841 T^{2} )^{2} \))
$67$ (\( 1 + 8809 T + 20151121 T^{2} \))(\( ( 1 - 5609 T + 20151121 T^{2} )^{2} \))(\( ( 1 + 5218 T + 20151121 T^{2} )^{2} \))
$71$ (\( ( 1 - 5041 T )( 1 + 5041 T ) \))(\( 1 - 31383362 T^{2} + 645753531245761 T^{4} \))(\( 1 - 7658462 T^{2} + 645753531245761 T^{4} \))
$73$ (\( 1 - 9791 T + 28398241 T^{2} \))(\( ( 1 - 7199 T + 28398241 T^{2} )^{2} \))(\( ( 1 + 4519 T + 28398241 T^{2} )^{2} \))
$79$ (\( 1 + 12361 T + 38950081 T^{2} \))(\( ( 1 - 329 T + 38950081 T^{2} )^{2} \))(\( ( 1 - 7502 T + 38950081 T^{2} )^{2} \))
$83$ (\( ( 1 - 6889 T )( 1 + 6889 T ) \))(\( 1 - 93167042 T^{2} + 2252292232139041 T^{4} \))(\( 1 - 64875281 T^{2} + 2252292232139041 T^{4} \))
$89$ (\( ( 1 - 7921 T )( 1 + 7921 T ) \))(\( 1 - 58951082 T^{2} + 3936588805702081 T^{4} \))(\( 1 - 46736606 T^{2} + 3936588805702081 T^{4} \))
$97$ (\( 1 - 9743 T + 88529281 T^{2} \))(\( ( 1 + 15961 T + 88529281 T^{2} )^{2} \))(\( ( 1 - 10571 T + 88529281 T^{2} )^{2} \))
show more
show less