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Properties

Label 142.2.c
Level $142$
Weight $2$
Character orbit 142.c
Rep. character $\chi_{142}(5,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $24$
Newform subspaces $3$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 142 = 2 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 142.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(142, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q - 4 q^{3} - 6 q^{4} - 4 q^{5} + 2 q^{9} + O(q^{10}) \) \( 24 q - 4 q^{3} - 6 q^{4} - 4 q^{5} + 2 q^{9} + 10 q^{11} + 6 q^{12} - 10 q^{13} + 2 q^{14} + 16 q^{15} - 6 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} + 16 q^{20} - 32 q^{21} - 14 q^{22} - 34 q^{25} + 12 q^{26} - 10 q^{27} + 6 q^{29} - 28 q^{30} - 2 q^{31} - 2 q^{33} + 48 q^{34} - 26 q^{35} - 8 q^{36} + 28 q^{37} - 16 q^{38} + 72 q^{41} - 28 q^{42} - 16 q^{43} - 10 q^{44} + 76 q^{45} - 20 q^{46} - 26 q^{47} - 4 q^{48} - 42 q^{49} - 20 q^{50} - 36 q^{51} - 10 q^{52} + 6 q^{53} + 18 q^{54} + 14 q^{55} - 8 q^{56} - 12 q^{57} + 10 q^{58} + 14 q^{59} + 16 q^{60} - 26 q^{61} + 24 q^{62} - 12 q^{63} - 6 q^{64} - 34 q^{65} + 56 q^{66} + 28 q^{67} - 4 q^{68} + 24 q^{69} - 4 q^{70} - 42 q^{71} + 24 q^{72} + 52 q^{73} - 4 q^{74} + 66 q^{75} + 18 q^{76} + 14 q^{77} + 6 q^{78} + 68 q^{79} - 4 q^{80} - 24 q^{82} - 28 q^{83} + 38 q^{84} - 44 q^{85} - 10 q^{86} + 8 q^{87} + 6 q^{88} - 48 q^{89} - 4 q^{90} + 72 q^{91} - 10 q^{92} - 16 q^{93} - 12 q^{94} + 4 q^{95} + 92 q^{97} + 16 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(142, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
142.2.c.a 142.c 71.c $4$ $1.134$ \(\Q(\zeta_{10})\) None 142.2.c.a \(1\) \(-3\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
142.2.c.b 142.c 71.c $8$ $1.134$ 8.0.159390625.1 None 142.2.c.b \(2\) \(1\) \(-5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}-\beta _{2}q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
142.2.c.c 142.c 71.c $12$ $1.134$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 142.2.c.c \(-3\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{4}+(-\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(142, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(142, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(71, [\chi])\)\(^{\oplus 2}\)