Properties

Label 35.6.b
Level $35$
Weight $6$
Character orbit 35.b
Rep. character $\chi_{35}(29,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 35.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(35, [\chi])\).

Total New Old
Modular forms 22 14 8
Cusp forms 18 14 4
Eisenstein series 4 0 4

Trace form

\( 14 q - 212 q^{4} + 156 q^{5} - 180 q^{6} - 796 q^{9} + O(q^{10}) \) \( 14 q - 212 q^{4} + 156 q^{5} - 180 q^{6} - 796 q^{9} + 904 q^{10} - 1158 q^{11} + 784 q^{14} - 2602 q^{15} + 9012 q^{16} - 1152 q^{19} - 3572 q^{20} - 2254 q^{21} - 24312 q^{24} - 494 q^{25} + 11908 q^{26} + 22342 q^{29} + 17212 q^{30} + 6548 q^{31} - 7180 q^{34} + 3038 q^{35} - 4356 q^{36} + 19574 q^{39} - 44540 q^{40} - 7044 q^{41} + 43648 q^{44} - 50208 q^{45} - 19456 q^{46} - 33614 q^{49} - 32796 q^{50} - 5186 q^{51} - 28164 q^{54} + 36892 q^{55} - 69972 q^{56} + 112716 q^{59} + 208164 q^{60} + 178784 q^{61} - 94084 q^{64} + 6418 q^{65} - 248836 q^{66} - 217972 q^{69} + 44492 q^{70} - 13952 q^{71} + 272160 q^{74} - 21432 q^{75} + 134608 q^{76} + 73090 q^{79} + 166596 q^{80} + 24142 q^{81} + 116032 q^{84} - 306686 q^{85} - 532960 q^{86} - 141328 q^{89} - 92492 q^{90} - 82418 q^{91} - 381388 q^{94} + 2560 q^{95} + 1024368 q^{96} + 173220 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.6.b.a 35.b 5.b $14$ $5.613$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(156\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)