Properties

Label 147.2.m
Level $147$
Weight $2$
Character orbit 147.m
Rep. character $\chi_{147}(4,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $108$
Newform subspaces $2$
Sturm bound $37$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.m (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(37\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(147, [\chi])\).

Total New Old
Modular forms 252 108 144
Cusp forms 204 108 96
Eisenstein series 48 0 48

Trace form

\( 108q + q^{3} + 8q^{4} - 2q^{5} - 4q^{6} + 5q^{7} + 12q^{8} + 9q^{9} + O(q^{10}) \) \( 108q + q^{3} + 8q^{4} - 2q^{5} - 4q^{6} + 5q^{7} + 12q^{8} + 9q^{9} - 4q^{10} - 20q^{11} + 2q^{12} - 2q^{13} - 2q^{14} - 10q^{15} - 2q^{16} - 14q^{17} - 55q^{19} - 48q^{20} - 4q^{21} + 10q^{22} - 8q^{23} - 42q^{24} - q^{25} - 26q^{26} - 2q^{27} - 50q^{28} + 16q^{29} - 8q^{30} - 75q^{31} - 106q^{32} - 2q^{33} - 112q^{34} - 26q^{35} - 16q^{36} - 44q^{37} + 58q^{38} + 8q^{39} + 28q^{40} + 76q^{41} + 66q^{42} + 14q^{43} + 84q^{44} + 26q^{45} - 24q^{46} + 8q^{47} + 64q^{48} + 45q^{49} - 188q^{50} + 52q^{51} + 86q^{52} + 40q^{53} + 2q^{54} - 36q^{55} + 168q^{56} + 6q^{57} + 14q^{58} + 16q^{59} + 68q^{60} + 17q^{61} + 20q^{62} - 8q^{63} - 36q^{64} - 30q^{65} - 4q^{66} - 21q^{67} - 68q^{70} - 60q^{71} - 48q^{72} - 45q^{73} - 62q^{74} - q^{75} - 46q^{76} - 34q^{77} - 28q^{78} - 17q^{79} + 50q^{80} + 9q^{81} + 50q^{82} + 58q^{83} - 2q^{84} + 24q^{85} + 84q^{86} - 10q^{87} + 174q^{88} + 86q^{89} + 8q^{90} + 5q^{91} + 84q^{92} - 3q^{93} + 128q^{94} + 186q^{95} - 92q^{96} - 44q^{97} + 346q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.2.m.a \(48\) \(1.174\) None \(-1\) \(-4\) \(0\) \(0\)
147.2.m.b \(60\) \(1.174\) None \(1\) \(5\) \(-2\) \(5\)

Decomposition of \(S_{2}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)