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Properties

Label 108.4.h
Level $108$
Weight $4$
Character orbit 108.h
Rep. character $\chi_{108}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 120 40 80
Cusp forms 96 32 64
Eisenstein series 24 8 16

Trace form

\( 32q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 32q + 3q^{2} - q^{4} + 6q^{5} - 20q^{10} - 2q^{13} + 78q^{14} - q^{16} + 234q^{20} + 15q^{22} + 198q^{25} - 132q^{28} - 78q^{29} - 687q^{32} - 191q^{34} - 8q^{37} - 891q^{38} + 34q^{40} + 156q^{41} + 48q^{46} + 194q^{49} + 1977q^{50} - 332q^{52} + 3006q^{56} - 314q^{58} - 2q^{61} + 410q^{64} - 690q^{65} - 4845q^{68} + 84q^{70} - 836q^{73} - 5874q^{74} - 495q^{76} - 978q^{77} + 682q^{82} + 248q^{85} + 8331q^{86} + 531q^{88} + 8724q^{92} + 168q^{94} + 16q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.h.a \(8\) \(6.372\) 8.0.\(\cdots\).1 None \(3\) \(0\) \(-66\) \(0\) \(q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
108.4.h.b \(24\) \(6.372\) None \(0\) \(0\) \(72\) \(0\)

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

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