Properties

Label 171.2.m
Level $171$
Weight $2$
Character orbit 171.m
Rep. character $\chi_{171}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 32 16 16
Eisenstein series 16 0 16

Trace form

\( 16q - 16q^{4} + 8q^{7} + O(q^{10}) \) \( 16q - 16q^{4} + 8q^{7} + 12q^{10} - 24q^{13} - 24q^{16} - 12q^{19} + 24q^{22} + 20q^{25} - 12q^{28} + 12q^{34} - 24q^{40} + 12q^{52} - 4q^{55} + 128q^{58} - 44q^{61} + 168q^{64} - 24q^{67} - 168q^{70} - 20q^{73} - 96q^{76} - 48q^{79} + 28q^{82} - 56q^{85} - 24q^{91} + 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
171.2.m.a \(16\) \(1.365\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{2}+(-\beta _{3}+2\beta _{4}+\beta _{10})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(171, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)