Properties

Label 108.3.c
Level 108
Weight 3
Character orbit c
Rep. character \(\chi_{108}(53,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 2
Sturm bound 54
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 45 3 42
Cusp forms 27 3 24
Eisenstein series 18 0 18

Trace form

\( 3q - 3q^{7} + O(q^{10}) \) \( 3q - 3q^{7} + 51q^{13} - 21q^{19} - 87q^{25} + 24q^{31} + 15q^{37} - 66q^{43} + 72q^{49} - 162q^{55} + 87q^{61} + 15q^{67} + 321q^{73} + 231q^{79} - 324q^{85} + 57q^{91} - 147q^{97} + O(q^{100}) \)

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.c.a \(1\) \(2.943\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(11\) \(q+11q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots\)
108.3.c.b \(2\) \(2.943\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-14\) \(q+iq^{5}-7q^{7}+iq^{11}+14q^{13}+2iq^{17}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 5 T )( 1 + 5 T ) \))(\( 1 + 31 T^{2} + 625 T^{4} \))
$7$ (\( 1 - 11 T + 49 T^{2} \))(\( ( 1 + 7 T + 49 T^{2} )^{2} \))
$11$ (\( ( 1 - 11 T )( 1 + 11 T ) \))(\( 1 - 161 T^{2} + 14641 T^{4} \))
$13$ (\( 1 - 23 T + 169 T^{2} \))(\( ( 1 - 14 T + 169 T^{2} )^{2} \))
$17$ (\( ( 1 - 17 T )( 1 + 17 T ) \))(\( 1 - 254 T^{2} + 83521 T^{4} \))
$19$ (\( 1 + 37 T + 361 T^{2} \))(\( ( 1 - 8 T + 361 T^{2} )^{2} \))
$23$ (\( ( 1 - 23 T )( 1 + 23 T ) \))(\( 1 + 238 T^{2} + 279841 T^{4} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( 1 - 1358 T^{2} + 707281 T^{4} \))
$31$ (\( 1 + 46 T + 961 T^{2} \))(\( ( 1 - 35 T + 961 T^{2} )^{2} \))
$37$ (\( 1 + 73 T + 1369 T^{2} \))(\( ( 1 - 44 T + 1369 T^{2} )^{2} \))
$41$ (\( ( 1 - 41 T )( 1 + 41 T ) \))(\( 1 - 2066 T^{2} + 2825761 T^{4} \))
$43$ (\( 1 + 22 T + 1849 T^{2} \))(\( ( 1 + 22 T + 1849 T^{2} )^{2} \))
$47$ (\( ( 1 - 47 T )( 1 + 47 T ) \))(\( 1 - 1502 T^{2} + 4879681 T^{4} \))
$53$ (\( ( 1 - 53 T )( 1 + 53 T ) \))(\( 1 - 5537 T^{2} + 7890481 T^{4} \))
$59$ (\( ( 1 - 59 T )( 1 + 59 T ) \))(\( 1 - 6638 T^{2} + 12117361 T^{4} \))
$61$ (\( 1 - 47 T + 3721 T^{2} \))(\( ( 1 - 20 T + 3721 T^{2} )^{2} \))
$67$ (\( 1 + 13 T + 4489 T^{2} \))(\( ( 1 - 14 T + 4489 T^{2} )^{2} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( 1 + 5794 T^{2} + 25411681 T^{4} \))
$73$ (\( 1 - 143 T + 5329 T^{2} \))(\( ( 1 - 89 T + 5329 T^{2} )^{2} \))
$79$ (\( 1 - 11 T + 6241 T^{2} \))(\( ( 1 - 110 T + 6241 T^{2} )^{2} \))
$83$ (\( ( 1 - 83 T )( 1 + 83 T ) \))(\( 1 - 13049 T^{2} + 47458321 T^{4} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( 1 - 15518 T^{2} + 62742241 T^{4} \))
$97$ (\( 1 + 169 T + 9409 T^{2} \))(\( ( 1 - 11 T + 9409 T^{2} )^{2} \))
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