Properties

Label 108.4.a
Level 108
Weight 4
Character orbit a
Rep. character \(\chi_{108}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 4
Sturm bound 72
Trace bound 7

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(108))\).

Total New Old
Modular forms 63 4 59
Cusp forms 45 4 41
Eisenstein series 18 0 18

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

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

Trace form

\( 4q - 22q^{7} + O(q^{10}) \) \( 4q - 22q^{7} + 14q^{13} + 140q^{19} - 338q^{25} + 98q^{31} + 662q^{37} - 1108q^{43} + 288q^{49} + 1134q^{55} - 742q^{61} - 292q^{67} - 868q^{73} - 4q^{79} + 1296q^{85} + 2272q^{91} - 112q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(108))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
108.4.a.a \(1\) \(6.372\) \(\Q\) None \(0\) \(0\) \(-9\) \(-1\) \(-\) \(+\) \(q-9q^{5}-q^{7}-63q^{11}-28q^{13}-72q^{17}+\cdots\)
108.4.a.b \(1\) \(6.372\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-37\) \(-\) \(+\) \(q-37q^{7}-19q^{13}-163q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.c \(1\) \(6.372\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(17\) \(-\) \(-\) \(q+17q^{7}+89q^{13}+107q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.d \(1\) \(6.372\) \(\Q\) None \(0\) \(0\) \(9\) \(-1\) \(-\) \(-\) \(q+9q^{5}-q^{7}+63q^{11}-28q^{13}+72q^{17}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(108))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(108)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 9 T + 125 T^{2} \))(\( 1 + 125 T^{2} \))(\( 1 + 125 T^{2} \))(\( 1 - 9 T + 125 T^{2} \))
$7$ (\( 1 + T + 343 T^{2} \))(\( 1 + 37 T + 343 T^{2} \))(\( 1 - 17 T + 343 T^{2} \))(\( 1 + T + 343 T^{2} \))
$11$ (\( 1 + 63 T + 1331 T^{2} \))(\( 1 + 1331 T^{2} \))(\( 1 + 1331 T^{2} \))(\( 1 - 63 T + 1331 T^{2} \))
$13$ (\( 1 + 28 T + 2197 T^{2} \))(\( 1 + 19 T + 2197 T^{2} \))(\( 1 - 89 T + 2197 T^{2} \))(\( 1 + 28 T + 2197 T^{2} \))
$17$ (\( 1 + 72 T + 4913 T^{2} \))(\( 1 + 4913 T^{2} \))(\( 1 + 4913 T^{2} \))(\( 1 - 72 T + 4913 T^{2} \))
$19$ (\( 1 - 98 T + 6859 T^{2} \))(\( 1 + 163 T + 6859 T^{2} \))(\( 1 - 107 T + 6859 T^{2} \))(\( 1 - 98 T + 6859 T^{2} \))
$23$ (\( 1 + 126 T + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 - 126 T + 12167 T^{2} \))
$29$ (\( 1 - 126 T + 24389 T^{2} \))(\( 1 + 24389 T^{2} \))(\( 1 + 24389 T^{2} \))(\( 1 + 126 T + 24389 T^{2} \))
$31$ (\( 1 + 259 T + 29791 T^{2} \))(\( 1 - 308 T + 29791 T^{2} \))(\( 1 - 308 T + 29791 T^{2} \))(\( 1 + 259 T + 29791 T^{2} \))
$37$ (\( 1 - 386 T + 50653 T^{2} \))(\( 1 - 323 T + 50653 T^{2} \))(\( 1 + 433 T + 50653 T^{2} \))(\( 1 - 386 T + 50653 T^{2} \))
$41$ (\( 1 - 450 T + 68921 T^{2} \))(\( 1 + 68921 T^{2} \))(\( 1 + 68921 T^{2} \))(\( 1 + 450 T + 68921 T^{2} \))
$43$ (\( 1 + 34 T + 79507 T^{2} \))(\( 1 + 520 T + 79507 T^{2} \))(\( 1 + 520 T + 79507 T^{2} \))(\( 1 + 34 T + 79507 T^{2} \))
$47$ (\( 1 - 54 T + 103823 T^{2} \))(\( 1 + 103823 T^{2} \))(\( 1 + 103823 T^{2} \))(\( 1 + 54 T + 103823 T^{2} \))
$53$ (\( 1 - 693 T + 148877 T^{2} \))(\( 1 + 148877 T^{2} \))(\( 1 + 148877 T^{2} \))(\( 1 + 693 T + 148877 T^{2} \))
$59$ (\( 1 + 180 T + 205379 T^{2} \))(\( 1 + 205379 T^{2} \))(\( 1 + 205379 T^{2} \))(\( 1 - 180 T + 205379 T^{2} \))
$61$ (\( 1 + 280 T + 226981 T^{2} \))(\( 1 - 719 T + 226981 T^{2} \))(\( 1 + 901 T + 226981 T^{2} \))(\( 1 + 280 T + 226981 T^{2} \))
$67$ (\( 1 + 586 T + 300763 T^{2} \))(\( 1 + 127 T + 300763 T^{2} \))(\( 1 - 1007 T + 300763 T^{2} \))(\( 1 + 586 T + 300763 T^{2} \))
$71$ (\( 1 + 504 T + 357911 T^{2} \))(\( 1 + 357911 T^{2} \))(\( 1 + 357911 T^{2} \))(\( 1 - 504 T + 357911 T^{2} \))
$73$ (\( 1 - 161 T + 389017 T^{2} \))(\( 1 + 919 T + 389017 T^{2} \))(\( 1 + 271 T + 389017 T^{2} \))(\( 1 - 161 T + 389017 T^{2} \))
$79$ (\( 1 - 440 T + 493039 T^{2} \))(\( 1 + 1387 T + 493039 T^{2} \))(\( 1 - 503 T + 493039 T^{2} \))(\( 1 - 440 T + 493039 T^{2} \))
$83$ (\( 1 + 999 T + 571787 T^{2} \))(\( 1 + 571787 T^{2} \))(\( 1 + 571787 T^{2} \))(\( 1 - 999 T + 571787 T^{2} \))
$89$ (\( 1 + 882 T + 704969 T^{2} \))(\( 1 + 704969 T^{2} \))(\( 1 + 704969 T^{2} \))(\( 1 - 882 T + 704969 T^{2} \))
$97$ (\( 1 + 721 T + 912673 T^{2} \))(\( 1 + 523 T + 912673 T^{2} \))(\( 1 - 1853 T + 912673 T^{2} \))(\( 1 + 721 T + 912673 T^{2} \))
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