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Properties

Label 176.6.j
Level $176$
Weight $6$
Character orbit 176.j
Rep. character $\chi_{176}(45,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 176.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(176, [\chi])\).

Total New Old
Modular forms 244 200 44
Cusp forms 236 200 36
Eisenstein series 8 0 8

Trace form

\( 200 q - 228 q^{6} - 492 q^{8} + O(q^{10}) \) \( 200 q - 228 q^{6} - 492 q^{8} + 868 q^{10} + 1572 q^{12} + 1240 q^{14} - 3600 q^{15} - 2440 q^{16} + 8020 q^{18} + 4720 q^{19} - 2148 q^{20} - 580 q^{24} - 7464 q^{27} + 2180 q^{28} + 63492 q^{30} + 23064 q^{31} + 3820 q^{32} - 3032 q^{34} - 4776 q^{35} - 9692 q^{36} - 69232 q^{38} - 119368 q^{40} - 20480 q^{42} - 4840 q^{44} + 121860 q^{46} - 88360 q^{47} + 248960 q^{48} - 480200 q^{49} + 132544 q^{50} + 4520 q^{51} - 49716 q^{52} - 116640 q^{54} - 161352 q^{56} - 163176 q^{58} + 44984 q^{59} + 239772 q^{60} + 96160 q^{61} + 342528 q^{62} + 243048 q^{64} - 55376 q^{65} + 99220 q^{66} + 89256 q^{67} + 29396 q^{68} - 44640 q^{69} - 619160 q^{70} - 485300 q^{72} - 199304 q^{74} - 127736 q^{75} - 54540 q^{76} + 859840 q^{78} + 355360 q^{79} + 369952 q^{80} - 1312200 q^{81} + 142696 q^{82} - 329240 q^{83} + 104956 q^{84} + 264800 q^{85} - 220720 q^{86} + 608588 q^{90} + 164720 q^{91} - 99300 q^{92} - 362352 q^{93} + 648880 q^{94} - 76848 q^{95} + 588452 q^{96} + 457912 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(176, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)