Properties

Label 154.2.k
Level $154$
Weight $2$
Character orbit 154.k
Rep. character $\chi_{154}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $32$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
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 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

Trace form

\( 32 q + 8 q^{4} + 10 q^{7} - 4 q^{9} + O(q^{10}) \) \( 32 q + 8 q^{4} + 10 q^{7} - 4 q^{9} - 4 q^{11} + 2 q^{14} - 24 q^{15} - 8 q^{16} + 4 q^{22} - 32 q^{23} + 20 q^{25} - 10 q^{28} - 20 q^{29} - 60 q^{35} - 16 q^{36} + 8 q^{37} - 20 q^{39} + 14 q^{42} - 16 q^{44} - 60 q^{51} + 16 q^{53} + 8 q^{56} + 80 q^{57} - 56 q^{58} - 16 q^{60} + 40 q^{63} + 8 q^{64} - 16 q^{67} + 16 q^{70} + 104 q^{71} + 40 q^{72} + 40 q^{74} - 4 q^{77} + 60 q^{79} + 60 q^{81} + 20 q^{84} - 80 q^{85} + 44 q^{86} + 16 q^{88} + 44 q^{91} - 28 q^{92} + 32 q^{93} + 100 q^{95} - 68 q^{99} + O(q^{100}) \)

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.k.a 154.k 77.l $32$ $1.230$ None 154.2.k.a \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$

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

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