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

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

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

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