Properties

Label 108.4.b
Level $108$
Weight $4$
Character orbit 108.b
Rep. character $\chi_{108}(107,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $72$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

Total New Old
Modular forms 60 24 36
Cusp forms 48 24 24
Eisenstein series 12 0 12

Trace form

\( 24q - 6q^{4} + O(q^{10}) \) \( 24q - 6q^{4} + 66q^{10} - 36q^{13} + 138q^{16} + 186q^{22} - 516q^{25} + 138q^{28} - 684q^{34} + 276q^{37} - 378q^{40} + 1056q^{46} - 432q^{49} + 1128q^{52} + 1884q^{58} - 828q^{61} - 570q^{64} - 5406q^{70} + 816q^{73} - 4428q^{76} + 1944q^{82} + 888q^{85} + 8190q^{88} + 4164q^{94} + 3048q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.4.b.a \(12\) \(6.372\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-1-\beta _{4})q^{4}-\beta _{9}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
108.4.b.b \(12\) \(6.372\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{6}q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)