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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.2.i.a 154.i 77.i $16$ $1.230$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 154.2.i.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots\)

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

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