↑

Properties

Label 342.10.n
Level $342$
Weight $10$
Character orbit 342.n
Rep. character $\chi_{342}(293,\cdot)$
Character field $\Q(\zeta_{6})$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 360 q + 92160 q^{4} - 3040 q^{6} + 684 q^{7} + 13870 q^{9} + O(q^{10}) \) \( 360 q + 92160 q^{4} - 3040 q^{6} + 684 q^{7} + 13870 q^{9} - 75525 q^{11} + 79440 q^{15} + 23592960 q^{16} + 1215354 q^{17} + 643725 q^{19} + 1585008 q^{22} - 778240 q^{24} + 70312500 q^{25} + 12075228 q^{27} + 175104 q^{28} - 10932120 q^{29} + 2615008 q^{30} - 5856570 q^{31} - 8193150 q^{33} + 3550720 q^{36} - 23763504 q^{38} + 47073390 q^{39} + 3053445 q^{41} + 46135360 q^{42} - 12893400 q^{43} - 19334400 q^{44} - 173719888 q^{45} + 178853286 q^{47} - 1046268900 q^{49} + 135152448 q^{50} + 24205005 q^{51} + 56625888 q^{53} + 177421472 q^{54} - 186797970 q^{57} - 173537271 q^{59} + 20336640 q^{60} - 162839880 q^{61} + 267542496 q^{62} + 168466628 q^{63} + 6039797760 q^{64} + 363235686 q^{65} - 56002880 q^{66} + 311130624 q^{68} + 412818294 q^{69} - 902316492 q^{71} - 302847669 q^{73} + 940174455 q^{75} + 164793600 q^{76} - 976155096 q^{77} + 748984128 q^{78} + 86124766 q^{81} - 274450896 q^{82} + 1225045284 q^{83} + 4892328042 q^{87} + 405762048 q^{88} - 1458870930 q^{89} - 518640000 q^{90} + 672791130 q^{91} - 291116352 q^{93} + 4054181268 q^{95} - 199229440 q^{96} + 3247809984 q^{98} + 4409016671 q^{99} + O(q^{100}) \)

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

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