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Properties

Label 154.2.f
Level $154$
Weight $2$
Character orbit 154.f
Rep. character $\chi_{154}(15,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $24$
Newform subspaces $5$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

Trace form

\( 24 q + 2 q^{2} + 8 q^{3} - 6 q^{4} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 10 q^{9} + O(q^{10}) \) \( 24 q + 2 q^{2} + 8 q^{3} - 6 q^{4} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 10 q^{9} - 10 q^{11} - 12 q^{12} + 4 q^{13} + 12 q^{15} - 6 q^{16} + 12 q^{17} - 2 q^{19} + 4 q^{20} - 8 q^{21} + 10 q^{22} - 24 q^{23} - 6 q^{24} - 30 q^{25} + 4 q^{26} + 26 q^{27} - 16 q^{29} - 20 q^{30} + 16 q^{31} - 8 q^{32} + 34 q^{33} + 28 q^{34} + 4 q^{35} - 4 q^{37} - 28 q^{38} - 24 q^{39} + 12 q^{41} - 52 q^{43} - 56 q^{45} - 8 q^{46} + 36 q^{47} + 8 q^{48} - 6 q^{49} - 10 q^{50} + 42 q^{51} - 16 q^{52} - 24 q^{53} + 64 q^{54} - 60 q^{55} - 10 q^{57} + 20 q^{58} - 66 q^{59} - 8 q^{60} + 24 q^{61} - 24 q^{62} - 6 q^{64} + 8 q^{65} + 8 q^{66} + 36 q^{67} + 12 q^{68} - 24 q^{69} + 8 q^{70} + 24 q^{71} + 10 q^{72} + 28 q^{73} + 52 q^{74} + 58 q^{75} + 28 q^{76} + 8 q^{77} + 32 q^{78} + 8 q^{79} + 4 q^{80} + 64 q^{81} + 14 q^{82} + 30 q^{83} - 8 q^{84} + 52 q^{85} - 14 q^{86} + 72 q^{87} + 10 q^{88} - 36 q^{89} - 28 q^{90} - 36 q^{91} + 16 q^{92} - 44 q^{93} + 32 q^{94} - 32 q^{95} + 4 q^{96} - 30 q^{97} - 8 q^{98} + 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.2.f.a 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.b 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(-1\) \(5\) \(3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.c 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.d 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(1\) \(5\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.e 154.f 11.c $8$ $1.230$ 8.0.58140625.2 None \(2\) \(-1\) \(5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(154, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)