Properties

Label 154.2.i
Level $154$
Weight $2$
Character orbit 154.i
Rep. character $\chi_{154}(87,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(154, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16q + 8q^{4} - 12q^{5} + 16q^{9} + O(q^{10}) \) \( 16q + 8q^{4} - 12q^{5} + 16q^{9} + 8q^{11} - 8q^{14} - 8q^{15} - 8q^{16} - 8q^{22} + 16q^{23} - 36q^{26} - 12q^{31} - 24q^{33} + 32q^{36} - 16q^{37} + 12q^{38} + 12q^{42} - 8q^{44} - 108q^{45} + 24q^{47} + 8q^{49} - 28q^{53} - 4q^{56} - 12q^{58} + 60q^{59} - 4q^{60} - 16q^{64} + 48q^{66} + 12q^{67} + 60q^{70} + 8q^{71} + 60q^{75} + 44q^{77} - 16q^{78} + 12q^{80} - 8q^{81} + 20q^{86} - 4q^{88} + 96q^{89} - 36q^{91} + 32q^{92} - 44q^{93} + 56q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(154, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
154.2.i.a \(16\) \(1.230\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-12\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(154, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)