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Properties

Label 147.3.d
Level $147$
Weight $3$
Character orbit 147.d
Rep. character $\chi_{147}(97,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 147.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(147, [\chi])\).

Total New Old
Modular forms 46 14 32
Cusp forms 30 14 16
Eisenstein series 16 0 16

Trace form

\( 14 q - 4 q^{2} + 44 q^{4} + 16 q^{8} - 42 q^{9} + O(q^{10}) \) \( 14 q - 4 q^{2} + 44 q^{4} + 16 q^{8} - 42 q^{9} - 36 q^{11} - 24 q^{15} + 76 q^{16} + 12 q^{18} - 36 q^{22} - 8 q^{23} - 38 q^{25} + 80 q^{29} - 80 q^{32} - 132 q^{36} - 22 q^{37} - 18 q^{39} - 118 q^{43} + 8 q^{44} + 72 q^{46} + 196 q^{50} + 24 q^{51} + 176 q^{53} + 102 q^{57} - 212 q^{58} + 108 q^{60} + 124 q^{64} + 268 q^{65} + 54 q^{67} + 84 q^{71} - 48 q^{72} - 604 q^{74} - 36 q^{78} - 134 q^{79} + 126 q^{81} - 640 q^{85} + 148 q^{86} - 284 q^{88} - 616 q^{92} + 378 q^{93} + 284 q^{95} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.3.d.a 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}-\zeta_{6}q^{3}+2\zeta_{6}q^{5}+2\zeta_{6}q^{6}+\cdots\)
147.3.d.b 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
147.3.d.c 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{2}+\zeta_{6}q^{3}+5q^{4}+3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
147.3.d.d 147.d 7.b $8$ $4.005$ 8.0.339738624.1 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+(5-\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)