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Properties

Label 35.5.h
Level $35$
Weight $5$
Character orbit 35.h
Rep. character $\chi_{35}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).

Total New Old
Modular forms 36 20 16
Cusp forms 28 20 8
Eisenstein series 8 0 8

Trace form

\( 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + O(q^{10}) \) \( 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + 90 q^{11} + 1266 q^{12} - 690 q^{14} + 100 q^{15} - 126 q^{16} - 864 q^{17} - 848 q^{18} - 1662 q^{19} + 1680 q^{21} + 2584 q^{22} - 1242 q^{23} + 1908 q^{24} + 1250 q^{25} - 1350 q^{26} - 134 q^{28} + 840 q^{29} + 800 q^{30} - 3636 q^{31} - 1758 q^{32} + 384 q^{33} + 150 q^{35} - 4164 q^{36} + 1068 q^{37} + 9180 q^{38} + 2976 q^{39} - 4146 q^{42} - 7692 q^{43} - 3618 q^{44} - 1800 q^{45} + 2038 q^{46} - 11412 q^{47} + 416 q^{49} + 1500 q^{50} + 6324 q^{51} - 7476 q^{52} + 1668 q^{53} + 33180 q^{54} + 13500 q^{56} + 15264 q^{57} + 1174 q^{58} + 216 q^{59} - 8250 q^{60} - 5856 q^{61} - 23632 q^{63} - 25788 q^{64} - 4650 q^{65} - 16248 q^{66} + 34 q^{67} - 6444 q^{68} + 900 q^{70} + 10488 q^{71} - 12052 q^{72} + 22776 q^{73} + 2538 q^{74} - 2250 q^{75} + 40488 q^{77} + 23784 q^{78} + 20788 q^{79} + 14400 q^{80} + 4154 q^{81} - 34146 q^{82} - 20316 q^{84} + 12000 q^{85} + 1980 q^{86} - 27474 q^{87} - 36148 q^{88} - 13176 q^{89} + 17976 q^{91} + 61404 q^{92} - 22908 q^{93} - 50610 q^{94} - 6900 q^{95} - 17460 q^{96} - 39606 q^{98} - 36716 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.5.h.a 35.h 7.d $20$ $3.618$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(6\) \(-18\) \(0\) \(-54\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)