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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.2.m.a 147.m 49.g $48$ $1.174$ None 147.2.m.a \(-1\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{21}]$
147.2.m.b 147.m 49.g $60$ $1.174$ None 147.2.m.b \(1\) \(5\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{21}]$

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

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