↑

Properties

Label 342.10.f
Level $342$
Weight $10$
Character orbit 342.f
Rep. character $\chi_{342}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $360$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 342.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(342, [\chi])\).

Total New Old
Modular forms 1088 360 728
Cusp forms 1072 360 712
Eisenstein series 16 0 16

Trace form

\( 360 q + 64 q^{2} - 146 q^{3} + 92160 q^{4} + 3040 q^{6} - 684 q^{7} + 16384 q^{8} + 13870 q^{9} + O(q^{10}) \) \( 360 q + 64 q^{2} - 146 q^{3} + 92160 q^{4} + 3040 q^{6} - 684 q^{7} + 16384 q^{8} + 13870 q^{9} + 25175 q^{11} - 37376 q^{12} - 129744 q^{13} - 307328 q^{14} - 26480 q^{15} + 23592960 q^{16} + 647330 q^{17} + 224096 q^{18} - 643725 q^{19} - 1288272 q^{21} + 528336 q^{22} + 2811848 q^{23} + 778240 q^{24} - 70312500 q^{25} + 4674544 q^{27} - 175104 q^{28} - 4843332 q^{29} + 1808800 q^{30} - 1952190 q^{31} + 4194304 q^{32} - 7611886 q^{33} + 9560160 q^{34} + 2087112 q^{35} + 3550720 q^{36} + 12953808 q^{37} + 11860816 q^{38} - 27002550 q^{39} - 68792377 q^{41} - 46135360 q^{42} - 19176624 q^{43} + 6444800 q^{44} + 37407200 q^{45} + 16995254 q^{47} - 9568256 q^{48} - 1046268900 q^{49} - 119248928 q^{50} - 2184155 q^{51} - 33214464 q^{52} - 75810476 q^{53} - 142856672 q^{54} - 78675968 q^{56} + 121701084 q^{57} + 151547609 q^{59} - 6778880 q^{60} + 162839880 q^{61} + 89180832 q^{62} + 551076544 q^{63} + 6039797760 q^{64} - 757207290 q^{65} - 492005760 q^{66} + 327999150 q^{67} + 165716480 q^{68} - 149598322 q^{69} + 469321444 q^{71} + 57368576 q^{72} - 387352107 q^{73} + 626189632 q^{74} + 966010497 q^{75} - 164793600 q^{76} - 244345624 q^{77} - 327214400 q^{78} - 242270280 q^{79} + 311577838 q^{81} + 274450896 q^{82} + 1011192094 q^{83} - 329797632 q^{84} + 181795008 q^{86} - 5211293266 q^{87} + 135254016 q^{88} - 2318948674 q^{89} - 882721600 q^{90} - 1939554630 q^{91} + 719833088 q^{92} - 667755584 q^{93} + 1050476424 q^{95} + 199229440 q^{96} + 1857589110 q^{97} - 577659360 q^{98} + 6614848423 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)