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Properties

Label 35.6.e
Level $35$
Weight $6$
Character orbit 35.e
Rep. character $\chi_{35}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 35.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 44 28 16
Cusp forms 36 28 8
Eisenstein series 8 0 8

Trace form

\( 28 q + 2 q^{2} - 18 q^{3} - 234 q^{4} - 50 q^{5} + 80 q^{6} + 138 q^{7} + 228 q^{8} - 1596 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{2} - 18 q^{3} - 234 q^{4} - 50 q^{5} + 80 q^{6} + 138 q^{7} + 228 q^{8} - 1596 q^{9} - 200 q^{10} + 804 q^{11} + 514 q^{12} + 3688 q^{13} + 2434 q^{14} - 1100 q^{15} - 6886 q^{16} - 3396 q^{17} - 2208 q^{18} + 1736 q^{19} + 8600 q^{20} - 490 q^{21} - 9312 q^{22} - 902 q^{23} + 9208 q^{24} - 8750 q^{25} + 4822 q^{26} + 19716 q^{27} - 10718 q^{28} + 23532 q^{29} + 3800 q^{30} + 2012 q^{31} - 21166 q^{32} - 1588 q^{33} - 77032 q^{34} + 100 q^{35} + 29148 q^{36} + 6360 q^{37} + 27648 q^{38} + 17948 q^{39} - 9600 q^{40} - 28188 q^{41} + 81342 q^{42} + 77460 q^{43} + 32638 q^{44} - 21000 q^{45} - 13382 q^{46} - 54756 q^{47} - 191452 q^{48} - 49822 q^{49} - 2500 q^{50} + 13220 q^{51} - 131140 q^{52} + 42352 q^{53} + 106572 q^{54} + 52200 q^{55} + 56184 q^{56} - 116704 q^{57} - 31442 q^{58} + 13848 q^{59} + 31350 q^{60} - 71474 q^{61} + 426024 q^{62} - 74560 q^{63} + 224084 q^{64} - 53600 q^{65} - 25220 q^{66} + 92122 q^{67} + 760 q^{68} - 202956 q^{69} + 99500 q^{70} + 59440 q^{71} - 404848 q^{72} - 49316 q^{73} - 231670 q^{74} - 11250 q^{75} - 116028 q^{76} + 174852 q^{77} + 355432 q^{78} + 171464 q^{79} - 150400 q^{80} - 80626 q^{81} + 164222 q^{82} + 480036 q^{83} - 590460 q^{84} + 15800 q^{85} - 53836 q^{86} - 200182 q^{87} - 159856 q^{88} + 55030 q^{89} + 90900 q^{90} - 75660 q^{91} - 235012 q^{92} + 249948 q^{93} + 473094 q^{94} + 48000 q^{95} + 525292 q^{96} - 538584 q^{97} - 989546 q^{98} + 412944 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.e.a 35.e 7.c $12$ $5.613$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(5\) \(-20\) \(150\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{4})q^{2}+(\beta _{1}+\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
35.6.e.b 35.e 7.c $16$ $5.613$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(2\) \(-200\) \(158\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(\beta _{1}-5^{2}\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)