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Properties

Label 342.10.bf
Level $342$
Weight $10$
Character orbit 342.bf
Rep. character $\chi_{342}(155,\cdot)$
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.bf (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

\( 1080 q + 219 q^{3} - 4560 q^{6} + 20805 q^{9} + O(q^{10}) \) \( 1080 q + 219 q^{3} - 4560 q^{6} + 20805 q^{9} + 194616 q^{13} - 804696 q^{15} - 4736016 q^{17} - 1243584 q^{18} - 670140 q^{19} + 1585008 q^{22} + 2334720 q^{24} - 10785969 q^{27} - 525312 q^{28} + 32796360 q^{29} - 15396387 q^{33} + 5326080 q^{36} + 71290512 q^{38} - 36633966 q^{39} - 9160335 q^{41} + 48105036 q^{43} - 171388170 q^{45} - 14352384 q^{48} + 6225985080 q^{49} + 345598848 q^{50} + 291757770 q^{51} - 49821696 q^{52} + 136055808 q^{54} - 494245272 q^{57} + 958344813 q^{59} + 206002176 q^{60} - 977039280 q^{61} + 625836972 q^{63} - 9059696640 q^{64} - 213902304 q^{66} + 1178992611 q^{67} + 456154200 q^{69} - 20066304 q^{72} + 1288812978 q^{73} + 974833248 q^{78} + 363405420 q^{79} - 2737559235 q^{81} + 823352688 q^{82} - 33770628 q^{87} + 4376612790 q^{89} - 1906366368 q^{90} + 1345582260 q^{91} - 3239248896 q^{92} + 123561408 q^{93} - 73856529 q^{97} + 9743429952 q^{98} - 13148742273 q^{99} + O(q^{100}) \)

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

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