Properties

Label 147.2.g
Level $147$
Weight $2$
Character orbit 147.g
Rep. character $\chi_{147}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $18$
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.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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 54 34 20
Cusp forms 22 18 4
Eisenstein series 32 16 16

Trace form

\( 18q + 3q^{3} + 6q^{4} - 5q^{9} + O(q^{10}) \) \( 18q + 3q^{3} + 6q^{4} - 5q^{9} - 6q^{12} - 16q^{15} + 20q^{16} - 16q^{18} + 9q^{19} - 32q^{22} + 13q^{25} - 24q^{30} - 15q^{31} + 4q^{36} - 17q^{37} - 5q^{39} + 22q^{43} - 32q^{46} + 24q^{51} + 6q^{52} - 46q^{57} + 24q^{60} - 12q^{61} + 32q^{64} + 37q^{67} + 32q^{72} + 27q^{73} + 15q^{75} + 80q^{78} - 3q^{79} + 15q^{81} - 32q^{85} - 32q^{88} + q^{93} + 96q^{99} + O(q^{100}) \)

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.g.a \(2\) \(1.174\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{9}+\cdots\)
147.2.g.b \(16\) \(1.174\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{13}q^{2}+(\beta _{7}-\beta _{9})q^{3}+(1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

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

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