Properties

Label 154.2.e
Level $154$
Weight $2$
Character orbit 154.e
Rep. character $\chi_{154}(23,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $6$
Sturm bound $48$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(13\)

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

\( 16 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 16 q^{9} + 8 q^{13} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 12 q^{17} + 8 q^{18} - 8 q^{20} + 16 q^{21} + 16 q^{23} - 4 q^{24} - 8 q^{25} + 12 q^{26} - 24 q^{27} + 4 q^{28} + 8 q^{29} - 8 q^{30} + 4 q^{31} + 4 q^{33} - 8 q^{34} + 4 q^{35} + 32 q^{36} + 8 q^{37} + 4 q^{38} + 4 q^{39} - 24 q^{41} - 20 q^{42} - 40 q^{43} - 4 q^{45} - 4 q^{46} - 16 q^{47} + 16 q^{49} - 32 q^{50} + 12 q^{51} - 4 q^{52} + 36 q^{53} - 16 q^{54} + 4 q^{56} - 56 q^{57} + 20 q^{58} + 4 q^{59} - 4 q^{60} - 36 q^{61} + 24 q^{62} - 20 q^{63} + 16 q^{64} + 4 q^{65} + 8 q^{66} - 4 q^{67} - 12 q^{68} + 24 q^{69} + 44 q^{70} - 8 q^{71} + 8 q^{72} + 16 q^{73} + 12 q^{74} + 60 q^{75} + 4 q^{77} - 16 q^{78} + 20 q^{79} + 4 q^{80} - 8 q^{81} + 8 q^{82} + 40 q^{83} + 4 q^{84} + 64 q^{85} + 4 q^{86} - 12 q^{87} + 72 q^{90} + 44 q^{91} - 32 q^{92} - 12 q^{93} + 8 q^{94} + 4 q^{95} - 4 q^{96} - 96 q^{97} - 48 q^{98} + O(q^{100}) \)

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.e.a 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.b 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.c 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.d 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.e 154.e 7.c $4$ $1.230$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
154.2.e.f 154.e 7.c $4$ $1.230$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)

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

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