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Properties

Label 342.10.g
Level $342$
Weight $10$
Character orbit 342.g
Rep. character $\chi_{342}(163,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $150$
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.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
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 1096 150 946
Cusp forms 1064 150 914
Eisenstein series 32 0 32

Trace form

\( 150 q + 16 q^{2} - 19200 q^{4} + 568 q^{5} + 10588 q^{7} - 8192 q^{8} + O(q^{10}) \) \( 150 q + 16 q^{2} - 19200 q^{4} + 568 q^{5} + 10588 q^{7} - 8192 q^{8} - 20000 q^{10} + 21638 q^{11} + 9760 q^{13} + 307232 q^{14} - 4915200 q^{16} + 997060 q^{17} - 82213 q^{19} - 290816 q^{20} - 47376 q^{22} + 221378 q^{23} - 29619871 q^{25} + 227392 q^{26} - 1355264 q^{28} + 3693680 q^{29} + 24830864 q^{31} + 1048576 q^{32} - 15012064 q^{34} - 1537812 q^{35} + 73027560 q^{37} + 5748480 q^{38} - 5120000 q^{40} - 5778765 q^{41} - 18193642 q^{43} - 2769664 q^{44} + 42368256 q^{46} - 101365240 q^{47} + 797132302 q^{49} - 18872160 q^{50} + 2498560 q^{52} + 77126604 q^{53} - 104597590 q^{55} - 157302784 q^{56} + 106622912 q^{58} + 330339487 q^{59} + 192074088 q^{61} - 39917632 q^{62} + 2516582400 q^{64} - 621895156 q^{65} - 722724705 q^{67} - 510494720 q^{68} + 50133312 q^{70} - 72791916 q^{71} - 320256101 q^{73} - 416386112 q^{74} + 483176192 q^{76} + 2682202636 q^{77} - 493875862 q^{79} + 37224448 q^{80} + 96055024 q^{82} + 431824670 q^{83} - 1008360654 q^{85} + 1204044032 q^{86} + 24256512 q^{88} - 1236780068 q^{89} - 798735984 q^{91} + 56672768 q^{92} + 1007004864 q^{94} - 990636514 q^{95} - 2755544831 q^{97} + 2668796944 q^{98} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)