Properties

Label 126.9.c
Level $126$
Weight $9$
Character orbit 126.c
Rep. character $\chi_{126}(55,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $3$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 200 28 172
Cusp forms 184 28 156
Eisenstein series 16 0 16

Trace form

\( 28 q + 3584 q^{4} - 1996 q^{7} + O(q^{10}) \) \( 28 q + 3584 q^{4} - 1996 q^{7} + 9216 q^{11} - 25344 q^{14} + 458752 q^{16} + 12288 q^{22} + 394272 q^{23} - 2647748 q^{25} - 255488 q^{28} + 961344 q^{29} - 373104 q^{35} - 2276120 q^{37} + 555880 q^{43} + 1179648 q^{44} + 4147200 q^{46} + 9620572 q^{49} - 27035136 q^{50} + 19012320 q^{53} - 3244032 q^{56} - 5769216 q^{58} + 58720256 q^{64} + 105662304 q^{65} - 45507880 q^{67} + 23265792 q^{70} - 67561920 q^{71} - 35555328 q^{74} - 70191936 q^{77} - 14914408 q^{79} + 172144800 q^{85} + 208253952 q^{86} + 1572864 q^{88} + 119247264 q^{91} + 50466816 q^{92} + 150384096 q^{95} - 159095808 q^{98} + O(q^{100}) \)

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.c.a $4$ $51.330$ 4.0.3520512.3 None \(0\) \(0\) \(0\) \(-6076\) \(q-2\beta _{3}q^{2}+2^{7}q^{4}+(-7\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
126.9.c.b $12$ $51.330$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-2340\) \(q-\beta _{1}q^{2}+2^{7}q^{4}+\beta _{2}q^{5}+(-195+\cdots)q^{7}+\cdots\)
126.9.c.c $12$ $51.330$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6420\) \(q-\beta _{1}q^{2}+2^{7}q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)

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

\( S_{9}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)