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Properties

Label 147.2.e
Level $147$
Weight $2$
Character orbit 147.e
Rep. character $\chi_{147}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $5$
Sturm bound $37$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(37\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 54 14 40
Cusp forms 22 14 8
Eisenstein series 32 0 32

Trace form

\( 14 q + 4 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 7 q^{9} + O(q^{10}) \) \( 14 q + 4 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 7 q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{15} - 6 q^{16} + 4 q^{18} + q^{19} + 8 q^{20} - 8 q^{22} + 8 q^{23} - q^{25} + 2 q^{26} - 2 q^{27} - 32 q^{29} + 9 q^{31} + 6 q^{32} - 2 q^{33} + 8 q^{36} + q^{37} + 2 q^{38} - 13 q^{39} + 20 q^{41} - 6 q^{43} + 20 q^{44} - 2 q^{45} + 24 q^{46} - 6 q^{47} + 8 q^{48} + 56 q^{50} + 4 q^{51} + 2 q^{52} - 16 q^{53} + 2 q^{54} - 8 q^{55} + 18 q^{57} - 12 q^{58} - 12 q^{59} + 8 q^{60} + 10 q^{61} - 36 q^{62} - 44 q^{64} - 30 q^{65} - 4 q^{66} - 3 q^{67} - 28 q^{71} + 6 q^{72} - 3 q^{73} - 10 q^{74} - q^{75} - 4 q^{76} - 36 q^{78} + q^{79} + 8 q^{80} - 7 q^{81} - 20 q^{82} - 12 q^{83} + 32 q^{85} - 50 q^{86} + 4 q^{87} - 48 q^{88} + 16 q^{89} + 8 q^{90} + 112 q^{92} + 7 q^{93} - 12 q^{94} + 34 q^{95} - 8 q^{96} + 12 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.2.e.a 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
147.2.e.b 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.c 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.d 147.e 7.c $4$ $1.174$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.e.e 147.e 7.c $4$ $1.174$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)