Properties

Label 126.4.f
Level $126$
Weight $4$
Character orbit 126.f
Rep. character $\chi_{126}(43,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $4$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

Total New Old
Modular forms 152 36 116
Cusp forms 136 36 100
Eisenstein series 16 0 16

Trace form

\( 36 q - 4 q^{2} - 6 q^{3} - 72 q^{4} - 16 q^{5} + 20 q^{6} + 32 q^{8} + 118 q^{9} + O(q^{10}) \) \( 36 q - 4 q^{2} - 6 q^{3} - 72 q^{4} - 16 q^{5} + 20 q^{6} + 32 q^{8} + 118 q^{9} - 86 q^{11} - 48 q^{12} - 56 q^{14} - 140 q^{15} - 288 q^{16} + 76 q^{17} - 192 q^{18} - 180 q^{19} - 64 q^{20} + 112 q^{21} + 36 q^{22} + 412 q^{23} + 80 q^{24} - 162 q^{25} + 36 q^{27} + 308 q^{29} - 176 q^{30} + 72 q^{31} - 64 q^{32} - 754 q^{33} - 180 q^{34} + 280 q^{35} - 680 q^{36} + 288 q^{37} - 188 q^{38} + 268 q^{39} + 522 q^{41} - 342 q^{43} + 688 q^{44} + 1316 q^{45} + 1188 q^{47} + 288 q^{48} - 882 q^{49} - 1076 q^{50} + 1274 q^{51} + 432 q^{53} - 2236 q^{54} + 1584 q^{55} - 224 q^{56} + 1422 q^{57} + 362 q^{59} + 544 q^{60} - 624 q^{62} + 420 q^{63} + 2304 q^{64} - 1872 q^{65} - 640 q^{66} - 1998 q^{67} - 152 q^{68} - 2608 q^{69} - 2216 q^{71} + 432 q^{72} - 828 q^{73} - 872 q^{74} + 3430 q^{75} + 360 q^{76} - 616 q^{77} + 200 q^{78} + 936 q^{79} + 512 q^{80} + 2086 q^{81} + 5832 q^{82} + 1384 q^{83} - 896 q^{84} - 936 q^{85} - 2132 q^{86} + 2248 q^{87} + 144 q^{88} - 3120 q^{89} - 760 q^{90} - 1008 q^{91} + 1648 q^{92} + 1300 q^{93} + 2308 q^{95} - 640 q^{96} - 3114 q^{97} + 392 q^{98} - 6644 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.4.f.a 126.f 9.c $6$ $7.434$ 6.0.309123.1 None \(6\) \(-12\) \(-9\) \(-21\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{5})q^{3}+(-4+\cdots)q^{4}+\cdots\)
126.4.f.b 126.f 9.c $8$ $7.434$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(9\) \(1\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{1})q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
126.4.f.c 126.f 9.c $10$ $7.434$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(4\) \(1\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
126.4.f.d 126.f 9.c $12$ $7.434$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-7\) \(-9\) \(-42\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{4})q^{2}+(-\beta _{4}+\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

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