Properties

Label 154.2.m
Level $154$
Weight $2$
Character orbit 154.m
Rep. character $\chi_{154}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $64$
Newform subspaces $3$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 224 64 160
Cusp forms 160 64 96
Eisenstein series 64 0 64

Trace form

\( 64 q + 8 q^{4} - 4 q^{5} - 8 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 64 q + 8 q^{4} - 4 q^{5} - 8 q^{6} - 2 q^{7} - 4 q^{9} - 20 q^{10} - 8 q^{13} - 2 q^{14} + 12 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} + 8 q^{20} - 16 q^{21} - 16 q^{23} + 4 q^{24} - 12 q^{25} + 8 q^{26} - 36 q^{27} - 14 q^{28} - 28 q^{29} + 8 q^{30} + 6 q^{31} + 46 q^{33} - 32 q^{34} - 34 q^{35} - 32 q^{36} - 8 q^{37} - 4 q^{38} - 24 q^{39} + 10 q^{40} - 56 q^{41} - 10 q^{42} + 40 q^{43} + 10 q^{44} + 4 q^{45} + 4 q^{46} - 44 q^{47} - 46 q^{49} + 32 q^{50} + 8 q^{51} + 4 q^{52} - 16 q^{53} - 64 q^{54} - 20 q^{55} - 4 q^{56} - 24 q^{57} + 20 q^{58} - 4 q^{59} + 4 q^{60} - 34 q^{61} + 16 q^{62} - 10 q^{63} - 16 q^{64} + 56 q^{65} + 32 q^{66} + 64 q^{67} + 2 q^{68} + 176 q^{69} + 6 q^{70} + 8 q^{71} + 12 q^{72} - 6 q^{73} + 8 q^{74} + 20 q^{75} + 40 q^{76} + 6 q^{77} + 96 q^{78} + 10 q^{79} + 6 q^{80} + 88 q^{81} + 12 q^{82} + 80 q^{83} + 36 q^{84} - 44 q^{85} + 26 q^{86} + 112 q^{87} + 10 q^{88} + 20 q^{89} + 88 q^{90} + 6 q^{91} - 28 q^{92} + 22 q^{93} + 52 q^{94} - 74 q^{95} + 4 q^{96} + 36 q^{97} + 48 q^{98} - 160 q^{99} + O(q^{100}) \)

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.m.a 154.m 77.m $8$ $1.230$ \(\Q(\zeta_{15})\) None 154.2.m.a \(-1\) \(1\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{15}]$ \(q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
154.2.m.b 154.m 77.m $24$ $1.230$ None 154.2.m.b \(-3\) \(-3\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{15}]$
154.2.m.c 154.m 77.m $32$ $1.230$ None 154.2.m.c \(4\) \(2\) \(-2\) \(7\) $\mathrm{SU}(2)[C_{15}]$

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

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