Properties

Label 126.9.p
Level $126$
Weight $9$
Character orbit 126.p
Rep. character $\chi_{126}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(216\)

Dimensions

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

Total New Old
Modular forms 392 128 264
Cusp forms 376 128 248
Eisenstein series 16 0 16

Trace form

\( 128 q + 16384 q^{4} + 1846 q^{7} + 13692 q^{9} + O(q^{10}) \) \( 128 q + 16384 q^{4} + 1846 q^{7} + 13692 q^{9} - 11388 q^{11} + 10110 q^{13} + 31488 q^{14} + 16518 q^{15} + 2097152 q^{16} - 63450 q^{17} - 271872 q^{18} + 638808 q^{21} - 22794 q^{23} + 5000000 q^{25} - 1262592 q^{26} + 265230 q^{27} + 236288 q^{28} + 1593096 q^{29} + 211968 q^{30} + 8260494 q^{35} + 1752576 q^{36} + 546986 q^{37} + 10333662 q^{39} - 3240612 q^{41} + 6650112 q^{42} - 1131328 q^{43} - 1457664 q^{44} + 12500304 q^{45} - 3708672 q^{46} - 3341302 q^{49} + 3694080 q^{50} + 3400074 q^{51} + 1294080 q^{52} - 6029676 q^{53} - 24685056 q^{54} + 4030464 q^{56} + 39152490 q^{57} + 7852800 q^{58} + 2114304 q^{60} - 100871130 q^{63} + 268435456 q^{64} - 71221956 q^{65} - 52829184 q^{66} + 44299780 q^{67} - 8121600 q^{68} - 77051310 q^{69} + 24680448 q^{70} + 145775388 q^{71} - 34799616 q^{72} - 3149568 q^{74} - 111281106 q^{75} + 220250082 q^{77} - 102752256 q^{78} - 59296556 q^{79} + 41389956 q^{81} + 421095780 q^{83} + 81767424 q^{84} + 57202500 q^{85} - 66786816 q^{86} + 319912860 q^{87} - 266243886 q^{89} + 415401984 q^{90} - 94376706 q^{91} - 2917632 q^{92} + 381509346 q^{93} + 233615328 q^{95} - 172693698 q^{97} - 177607680 q^{98} - 172487358 q^{99} + O(q^{100}) \)

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

The newforms in this space have not yet been added to the LMFDB.

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

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