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 $1$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
154.2.m.a \(8\) \(1.230\) \(\Q(\zeta_{15})\) None \(-1\) \(1\) \(-5\) \(-4\) \(q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
154.2.m.b \(24\) \(1.230\) None \(-3\) \(-3\) \(3\) \(-5\)
154.2.m.c \(32\) \(1.230\) None \(4\) \(2\) \(-2\) \(7\)

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

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