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Properties

Label 342.10.h
Level $342$
Weight $10$
Character orbit 342.h
Rep. character $\chi_{342}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $360$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 342.h (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

\( 360 q - 32 q^{2} + 73 q^{3} - 46080 q^{4} - 1520 q^{6} - 684 q^{7} + 16384 q^{8} - 6935 q^{9} + O(q^{10}) \) \( 360 q - 32 q^{2} + 73 q^{3} - 46080 q^{4} - 1520 q^{6} - 684 q^{7} + 16384 q^{8} - 6935 q^{9} + 25175 q^{11} - 37376 q^{12} + 64872 q^{13} + 614656 q^{14} - 389108 q^{15} - 11796480 q^{16} + 647330 q^{17} + 224096 q^{18} - 643725 q^{19} - 1288272 q^{21} - 1056672 q^{22} - 1405924 q^{23} - 389120 q^{24} + 140625000 q^{25} + 4674544 q^{27} - 175104 q^{28} + 9686664 q^{29} + 1808800 q^{30} - 1952190 q^{31} - 2097152 q^{32} + 22455371 q^{33} - 19120320 q^{34} + 2087112 q^{35} - 1775360 q^{36} + 12953808 q^{37} + 5951344 q^{38} - 27002550 q^{39} + 137584754 q^{41} + 9796256 q^{42} + 9588312 q^{43} + 6444800 q^{44} + 37407200 q^{45} - 33990508 q^{47} + 4784128 q^{48} - 1046268900 q^{49} - 119248928 q^{50} + 144650980 q^{51} + 16607232 q^{52} - 75810476 q^{53} + 98308960 q^{54} - 78675968 q^{56} + 209673219 q^{57} - 303095218 q^{59} + 106390528 q^{60} - 325679760 q^{61} + 89180832 q^{62} - 1224481778 q^{63} + 6039797760 q^{64} - 757207290 q^{65} + 471112752 q^{66} - 163999575 q^{67} + 165716480 q^{68} - 149598322 q^{69} + 469321444 q^{71} + 77434880 q^{72} - 387352107 q^{73} - 313094816 q^{74} + 966010497 q^{75} + 158031360 q^{76} - 244345624 q^{77} - 617690336 q^{78} + 121135140 q^{79} - 1874103863 q^{81} + 274450896 q^{82} + 1011192094 q^{83} - 329797632 q^{84} - 90897504 q^{86} - 5211293266 q^{87} + 135254016 q^{88} - 2318948674 q^{89} + 2081422496 q^{90} - 1939554630 q^{91} - 359916544 q^{92} - 3953302766 q^{93} + 962417418 q^{95} + 199229440 q^{96} - 928794555 q^{97} - 577659360 q^{98} + 648788896 q^{99} + O(q^{100}) \)

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

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