Properties

Label 126.9.s
Level $126$
Weight $9$
Character orbit 126.s
Rep. character $\chi_{126}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $2$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 400 40 360
Cusp forms 368 40 328
Eisenstein series 32 0 32

Trace form

\( 40 q + 2560 q^{4} + 68 q^{7} + O(q^{10}) \) \( 40 q + 2560 q^{4} + 68 q^{7} + 11776 q^{10} + 151368 q^{13} - 327680 q^{16} - 87268 q^{19} + 81920 q^{22} + 1153916 q^{25} - 96256 q^{28} - 5100972 q^{31} - 3653632 q^{34} + 3706964 q^{37} - 1507328 q^{40} + 5325704 q^{43} + 6422528 q^{46} - 41835428 q^{49} + 9687552 q^{52} - 18881344 q^{55} + 16440832 q^{58} - 70986672 q^{61} - 83886080 q^{64} + 52674700 q^{67} - 40308736 q^{70} - 148449164 q^{73} - 22340608 q^{76} - 72836820 q^{79} - 133189632 q^{82} + 112996352 q^{85} + 5242880 q^{88} - 511983852 q^{91} + 74222592 q^{94} - 389268176 q^{97} + O(q^{100}) \)

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.s.a $20$ $51.330$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-3710\) \(q-8\beta _{3}q^{2}+(2^{7}+2^{7}\beta _{5})q^{4}+(19\beta _{3}+\cdots)q^{5}+\cdots\)
126.9.s.b $20$ $51.330$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(3778\) \(q-8\beta _{2}q^{2}+(2^{7}+2^{7}\beta _{6})q^{4}+(-93\beta _{2}+\cdots)q^{5}+\cdots\)

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

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