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Properties

Label 342.10.x
Level $342$
Weight $10$
Character orbit 342.x
Rep. character $\chi_{342}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1080$
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.x (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 3264 1080 2184
Cusp forms 3216 1080 2136
Eisenstein series 48 0 48

Trace form

\( 1080 q - 438 q^{3} + 9120 q^{6} - 41610 q^{9} + O(q^{10}) \) \( 1080 q - 438 q^{3} + 9120 q^{6} - 41610 q^{9} + 194616 q^{13} + 283188 q^{15} + 4736016 q^{17} + 1243584 q^{18} - 670140 q^{19} + 1585008 q^{22} + 12653316 q^{23} - 1167360 q^{24} - 10785969 q^{27} - 525312 q^{28} - 37402692 q^{33} - 10652160 q^{36} - 36633966 q^{39} - 24052518 q^{43} + 105258366 q^{45} - 14352384 q^{48} - 3112992540 q^{49} + 691197696 q^{50} + 291757770 q^{51} + 99643392 q^{52} + 136055808 q^{54} - 204639168 q^{57} + 218866500 q^{59} + 206002176 q^{60} + 488519640 q^{61} + 45099426 q^{63} - 9059696640 q^{64} - 716683344 q^{66} - 2357985222 q^{67} - 139514112 q^{68} - 20066304 q^{72} + 1288812978 q^{73} + 2544238272 q^{78} - 726810840 q^{79} + 6112041486 q^{81} + 823352688 q^{82} - 284445936 q^{83} + 1484089344 q^{84} + 4240593522 q^{87} - 4376612790 q^{89} + 721300704 q^{90} + 1345582260 q^{91} + 6011509674 q^{93} - 5306523894 q^{95} + 147713058 q^{97} - 9743429952 q^{98} - 1817581173 q^{99} + O(q^{100}) \)

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

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