Properties

Label 126.3.b
Level $126$
Weight $3$
Character orbit 126.b
Rep. character $\chi_{126}(71,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 56 4 52
Cusp forms 40 4 36
Eisenstein series 16 0 16

Trace form

\( 4 q - 8 q^{4} + O(q^{10}) \) \( 4 q - 8 q^{4} + 8 q^{10} - 32 q^{13} + 16 q^{16} + 80 q^{19} + 16 q^{22} - 132 q^{25} + 16 q^{31} - 104 q^{34} + 152 q^{37} - 16 q^{40} + 80 q^{43} + 16 q^{46} + 28 q^{49} + 64 q^{52} - 464 q^{55} + 152 q^{58} + 232 q^{61} - 32 q^{64} - 192 q^{67} + 112 q^{70} - 96 q^{73} - 160 q^{76} + 304 q^{79} - 216 q^{82} + 328 q^{85} - 32 q^{88} + 112 q^{91} - 96 q^{94} - 288 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.b.a $4$ $3.433$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)