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Properties

Label 39.11.i
Level $39$
Weight $11$
Character orbit 39.i
Rep. character $\chi_{39}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $90$
Newform subspaces $2$
Sturm bound $51$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 39.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(51\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(39, [\chi])\).

Total New Old
Modular forms 98 98 0
Cusp forms 90 90 0
Eisenstein series 8 8 0

Trace form

\( 90 q - q^{3} + 22526 q^{4} - 10656 q^{6} - 17561 q^{7} - 39711 q^{9} + O(q^{10}) \) \( 90 q - q^{3} + 22526 q^{4} - 10656 q^{6} - 17561 q^{7} - 39711 q^{9} - 115926 q^{10} - 493104 q^{12} - 28757 q^{13} - 418018 q^{15} - 10401902 q^{16} - 3914600 q^{18} - 2127198 q^{19} + 19360658 q^{21} + 245488 q^{22} - 183648 q^{24} - 159290162 q^{25} + 19216766 q^{27} + 69311616 q^{28} + 4621522 q^{30} + 145299706 q^{31} + 85104140 q^{33} + 28576660 q^{34} + 101399522 q^{36} - 29480496 q^{37} - 120245358 q^{39} - 143894956 q^{40} + 151729230 q^{42} - 200021333 q^{43} + 136489288 q^{45} - 119290028 q^{46} - 1168840552 q^{48} - 1560531830 q^{49} + 155344468 q^{51} + 2297230092 q^{52} - 2963705436 q^{54} + 670559032 q^{55} - 309336036 q^{57} - 669043882 q^{58} - 3876518556 q^{60} + 3230933893 q^{61} + 1797842305 q^{63} - 4125430868 q^{64} + 10682701596 q^{66} + 5879515575 q^{67} + 3617037056 q^{69} - 3628350944 q^{70} + 1429801788 q^{72} + 9330704518 q^{73} + 9822845135 q^{75} + 2017883792 q^{76} - 18973296160 q^{78} - 6388830566 q^{79} + 9324137445 q^{81} - 20670703002 q^{82} + 9410797070 q^{84} + 19938369658 q^{85} + 14709616564 q^{87} - 22028879148 q^{88} - 32491634532 q^{90} + 15705307891 q^{91} - 6078941001 q^{93} - 10976591816 q^{94} + 37578941408 q^{96} - 26907298557 q^{97} - 98745056220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.11.i.a 39.i 39.i $2$ $24.779$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(243\) \(0\) \(-10907\) $\mathrm{U}(1)[D_{6}]$ \(q+3^{5}\zeta_{6}q^{3}+(-2^{10}+2^{10}\zeta_{6})q^{4}+\cdots\)
39.11.i.b 39.i 39.i $88$ $24.779$ None \(0\) \(-244\) \(0\) \(-6654\) $\mathrm{SU}(2)[C_{6}]$