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Properties

Label 116.6.e
Level $116$
Weight $6$
Character orbit 116.e
Rep. character $\chi_{116}(75,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $146$
Sturm bound $90$

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Defining parameters

Level: \( N \) \(=\) \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 116.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 116 \)
Character field: \(\Q(i)\)
Sturm bound: \(90\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(116, [\chi])\).

Total New Old
Modular forms 154 154 0
Cusp forms 146 146 0
Eisenstein series 8 8 0

Trace form

\( 146 q - 606 q^{8} + O(q^{10}) \) \( 146 q - 606 q^{8} + 62 q^{10} - 1274 q^{12} - 1016 q^{14} - 4184 q^{16} - 1014 q^{17} - 2934 q^{18} + 4092 q^{20} - 672 q^{21} + 104 q^{24} - 65678 q^{25} + 11566 q^{26} - 7964 q^{29} + 38076 q^{30} - 15610 q^{32} + 38520 q^{36} - 11890 q^{37} + 27898 q^{40} + 6186 q^{41} + 31706 q^{44} + 24992 q^{45} - 42652 q^{46} - 79430 q^{48} - 256146 q^{49} + 5466 q^{50} - 32552 q^{52} + 63880 q^{53} + 86504 q^{54} + 19840 q^{56} + 160432 q^{58} + 132406 q^{60} - 33226 q^{61} + 24992 q^{65} - 160702 q^{66} - 19316 q^{68} + 21808 q^{69} - 170884 q^{70} + 12816 q^{72} - 26170 q^{73} + 95284 q^{74} + 270592 q^{76} + 109696 q^{77} + 382640 q^{78} - 1196362 q^{81} - 91824 q^{82} + 90940 q^{84} - 90056 q^{85} + 521556 q^{88} + 299002 q^{89} - 69480 q^{90} + 1010660 q^{94} - 127602 q^{97} + 444424 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(116, [\chi])\) into newform subspaces

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