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Properties

Label 147.6.i
Level $147$
Weight $6$
Character orbit 147.i
Rep. character $\chi_{147}(22,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $276$
Sturm bound $112$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.i (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(112\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(147, [\chi])\).

Total New Old
Modular forms 576 276 300
Cusp forms 552 276 276
Eisenstein series 24 0 24

Trace form

\( 276 q - 18 q^{3} - 704 q^{4} - 44 q^{5} - 72 q^{6} + 138 q^{7} - 492 q^{8} - 3726 q^{9} + O(q^{10}) \) \( 276 q - 18 q^{3} - 704 q^{4} - 44 q^{5} - 72 q^{6} + 138 q^{7} - 492 q^{8} - 3726 q^{9} + 1164 q^{10} - 830 q^{11} - 864 q^{12} - 1188 q^{13} + 838 q^{14} - 990 q^{15} - 8720 q^{16} + 4078 q^{17} + 16928 q^{19} + 16308 q^{20} + 1242 q^{21} + 3300 q^{22} + 5104 q^{23} - 3186 q^{24} - 34786 q^{25} - 4460 q^{26} - 1458 q^{27} - 27588 q^{28} - 992 q^{29} - 2736 q^{30} + 64308 q^{31} + 54380 q^{32} + 9792 q^{33} - 50628 q^{34} + 14464 q^{35} - 57024 q^{36} + 19266 q^{37} + 10192 q^{38} + 26190 q^{39} - 149324 q^{40} - 58592 q^{41} - 39960 q^{42} + 21028 q^{43} + 49224 q^{44} + 8910 q^{45} + 40360 q^{46} + 9902 q^{47} + 238320 q^{48} + 85550 q^{49} + 487348 q^{50} + 26100 q^{51} + 54988 q^{52} - 63356 q^{53} - 5832 q^{54} - 197170 q^{55} - 292194 q^{56} + 32220 q^{57} - 76188 q^{58} + 139072 q^{59} + 40860 q^{60} + 89318 q^{61} + 149648 q^{62} + 21384 q^{63} - 487152 q^{64} + 150684 q^{65} - 98568 q^{66} + 46536 q^{67} - 30348 q^{68} + 39960 q^{69} - 186450 q^{70} - 398388 q^{71} + 99630 q^{72} + 124842 q^{73} + 185692 q^{74} - 59886 q^{75} + 124674 q^{76} - 21202 q^{77} - 90468 q^{78} + 1760 q^{79} + 2082488 q^{80} - 301806 q^{81} - 271872 q^{82} - 299798 q^{83} + 43776 q^{84} - 231816 q^{85} - 1564920 q^{86} + 125370 q^{87} - 1698840 q^{88} - 195142 q^{89} + 94284 q^{90} + 602404 q^{91} + 224994 q^{92} - 192420 q^{93} + 464918 q^{94} + 407412 q^{95} - 21204 q^{96} - 1267900 q^{97} + 3028084 q^{98} + 22356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)