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Properties

Label 126.10.t
Level $126$
Weight $10$
Character orbit 126.t
Rep. character $\chi_{126}(47,\cdot)$
Character field $\Q(\zeta_{6})$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 144 q + 18432 q^{4} - 684 q^{7} - 18594 q^{9} + O(q^{10}) \) \( 144 q + 18432 q^{4} - 684 q^{7} - 18594 q^{9} - 194616 q^{13} + 191136 q^{14} - 91164 q^{15} - 4718592 q^{16} - 1578672 q^{17} - 509760 q^{18} - 1246374 q^{21} + 1744896 q^{24} + 56250000 q^{25} - 5511360 q^{26} + 3783474 q^{27} + 175104 q^{28} + 2908374 q^{29} + 5427936 q^{30} - 5856570 q^{31} + 9483444 q^{33} + 31253820 q^{35} - 8217600 q^{36} + 6476904 q^{37} + 57636816 q^{39} - 3347706 q^{41} - 11674656 q^{42} - 8017506 q^{43} - 23672832 q^{44} - 102569262 q^{45} + 6429024 q^{46} + 58029246 q^{47} - 53538372 q^{49} - 19952832 q^{50} + 99937230 q^{51} - 183818772 q^{53} + 82294560 q^{54} + 28714236 q^{57} + 102973248 q^{58} - 72955500 q^{59} - 67012608 q^{60} - 525203082 q^{61} - 46310976 q^{62} - 185002740 q^{63} - 2415919104 q^{64} - 3739260 q^{65} + 258104064 q^{66} - 278498556 q^{67} - 808280064 q^{68} - 923244168 q^{69} + 192824064 q^{70} + 24379392 q^{72} + 304867380 q^{75} - 1764252972 q^{77} - 964663296 q^{78} - 462584394 q^{79} - 638456382 q^{81} - 1160538624 q^{84} + 510030000 q^{85} - 1361534574 q^{87} - 870224934 q^{89} - 3409067808 q^{90} - 1081909170 q^{91} - 2385020928 q^{92} + 3084121668 q^{93} - 2477994546 q^{95} + 446693376 q^{96} - 1356263568 q^{97} + 2537884032 q^{98} + 6346439964 q^{99} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)