Properties

Label 126.9.b
Level $126$
Weight $9$
Character orbit 126.b
Rep. character $\chi_{126}(71,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $216$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(126, [\chi])\).

Total New Old
Modular forms 200 16 184
Cusp forms 184 16 168
Eisenstein series 16 0 16

Trace form

\( 16 q - 2048 q^{4} + O(q^{10}) \) \( 16 q - 2048 q^{4} - 7168 q^{10} + 76720 q^{13} + 262144 q^{16} + 575120 q^{19} - 404480 q^{22} - 1964352 q^{25} - 920528 q^{31} + 2953216 q^{34} + 1798640 q^{37} + 917504 q^{40} - 28855168 q^{43} + 18780160 q^{46} + 13176688 q^{49} - 9820160 q^{52} + 59105872 q^{55} - 8922112 q^{58} - 9602768 q^{61} - 33554432 q^{64} + 422928 q^{67} - 41796608 q^{70} + 89144160 q^{73} - 73615360 q^{76} - 267458576 q^{79} - 31223808 q^{82} + 249261040 q^{85} + 51773440 q^{88} - 25661888 q^{91} + 168290304 q^{94} + 195562752 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.9.b.a $8$ $51.330$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-8\beta _{2}q^{2}-2^{7}q^{4}+(-91\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
126.9.b.b $8$ $51.330$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-8\beta _{2}q^{2}-2^{7}q^{4}+(34\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)