Properties

Label 108.3.f
Level $108$
Weight $3$
Character orbit 108.f
Rep. character $\chi_{108}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $3$
Sturm bound $54$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(54\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

Total New Old
Modular forms 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

Trace form

\( 20 q + q^{2} - q^{4} + 2 q^{5} + 22 q^{8} + O(q^{10}) \) \( 20 q + q^{2} - q^{4} + 2 q^{5} + 22 q^{8} + 4 q^{10} - 2 q^{13} + 24 q^{14} - q^{16} + 32 q^{17} - 52 q^{20} - 9 q^{22} - 12 q^{25} - 160 q^{26} - 36 q^{28} + 26 q^{29} - 119 q^{32} - 11 q^{34} - 8 q^{37} + 153 q^{38} + 4 q^{40} - 58 q^{41} + 390 q^{44} - 96 q^{46} - 16 q^{49} + 237 q^{50} + 22 q^{52} - 136 q^{53} - 270 q^{56} + 52 q^{58} - 2 q^{61} - 564 q^{62} + 2 q^{64} - 146 q^{65} - 331 q^{68} + 102 q^{70} + 16 q^{73} + 404 q^{74} + 93 q^{76} + 246 q^{77} + 848 q^{80} + 202 q^{82} - 52 q^{85} + 447 q^{86} + 75 q^{88} + 392 q^{89} - 426 q^{92} + 48 q^{94} - 62 q^{97} - 1022 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.3.f.a 108.f 36.f $2$ $2.943$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-2q^{2}+4q^{4}+(4-4\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)
108.3.f.b 108.f 36.f $2$ $2.943$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
108.3.f.c 108.f 36.f $16$ $2.943$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

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