Properties

Label 108.2.a
Level $108$
Weight $2$
Character orbit 108.a
Rep. character $\chi_{108}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(108))\).

Total New Old
Modular forms 27 1 26
Cusp forms 10 1 9
Eisenstein series 17 0 17

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.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 5q^{7} + O(q^{10}) \) \( q + 5q^{7} - 7q^{13} - q^{19} - 5q^{25} - 4q^{31} - q^{37} + 8q^{43} + 18q^{49} - 13q^{61} + 11q^{67} + 17q^{73} - 13q^{79} - 35q^{91} + 5q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(108))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
108.2.a.a \(1\) \(0.862\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(-\) \(+\) \(q+5q^{7}-7q^{13}-q^{19}-5q^{25}-4q^{31}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(108))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(108)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)