Properties

Label 108.4.a
Level $108$
Weight $4$
Character orbit 108.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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
108.4.a.a 108.a 1.a $1$ $6.372$ \(\Q\) None 108.4.a.a \(0\) \(0\) \(-9\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-9q^{5}-q^{7}-63q^{11}-28q^{13}-72q^{17}+\cdots\)
108.4.a.b 108.a 1.a $1$ $6.372$ \(\Q\) \(\Q(\sqrt{-3}) \) 108.4.a.b \(0\) \(0\) \(0\) \(-37\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-37q^{7}-19q^{13}-163q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.c 108.a 1.a $1$ $6.372$ \(\Q\) \(\Q(\sqrt{-3}) \) 108.4.a.c \(0\) \(0\) \(0\) \(17\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+17q^{7}+89q^{13}+107q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.d 108.a 1.a $1$ $6.372$ \(\Q\) None 108.4.a.a \(0\) \(0\) \(9\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+9q^{5}-q^{7}+63q^{11}-28q^{13}+72q^{17}+\cdots\)

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

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