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Properties

Label 126.10.e
Level $126$
Weight $10$
Character orbit 126.e
Rep. character $\chi_{126}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 126.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(126, [\chi])\).

Total New Old
Modular forms 440 144 296
Cusp forms 424 144 280
Eisenstein series 16 0 16

Trace form

\( 144 q + 36864 q^{4} - 2500 q^{5} + 4544 q^{6} + 684 q^{7} - 35492 q^{9} + O(q^{10}) \) \( 144 q + 36864 q^{4} - 2500 q^{5} + 4544 q^{6} + 684 q^{7} - 35492 q^{9} - 30824 q^{11} + 64872 q^{13} - 63712 q^{14} - 438836 q^{15} + 9437184 q^{16} - 141944 q^{17} + 604992 q^{18} + 446760 q^{19} - 640000 q^{20} + 176968 q^{21} + 3105496 q^{23} + 1163264 q^{24} - 28125000 q^{25} - 7320832 q^{26} - 9311310 q^{27} + 175104 q^{28} + 7963310 q^{29} - 9683648 q^{30} + 3904380 q^{31} - 44004040 q^{33} - 14047304 q^{35} - 9085952 q^{36} - 6476904 q^{37} - 25021632 q^{38} - 6052634 q^{39} - 8594034 q^{41} - 11484864 q^{42} + 8017506 q^{43} - 7890944 q^{44} + 76908266 q^{45} - 6429024 q^{46} - 38686164 q^{47} - 22466826 q^{49} - 6650944 q^{50} + 77910584 q^{51} + 16607232 q^{52} + 216121452 q^{53} + 105942752 q^{54} - 38366892 q^{55} - 16310272 q^{56} + 172540308 q^{57} - 51486624 q^{58} + 242179664 q^{59} - 112342016 q^{60} - 301224132 q^{61} + 488279744 q^{62} + 327191994 q^{63} + 2415919104 q^{64} + 182147160 q^{65} - 164874496 q^{66} + 556997112 q^{67} - 36337664 q^{68} - 1167842728 q^{69} - 275355936 q^{70} - 886969280 q^{71} + 154877952 q^{72} + 690199776 q^{73} - 197766240 q^{74} - 762413594 q^{75} + 114370560 q^{76} - 994171012 q^{77} - 341992960 q^{78} - 1409709348 q^{79} - 163840000 q^{80} + 784985320 q^{81} - 665503844 q^{83} + 45303808 q^{84} - 510030000 q^{85} + 282806976 q^{86} + 2838137188 q^{87} - 957941082 q^{89} - 799787488 q^{90} - 633381750 q^{91} + 795006976 q^{92} - 4186445888 q^{93} - 1515390336 q^{94} + 1622785372 q^{95} + 297795584 q^{96} + 452087856 q^{97} + 4185630336 q^{98} + 1035499612 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(126, [\chi]) \cong \)