Properties

Label 58.2.e
Level $58$
Weight $2$
Character orbit 58.e
Rep. character $\chi_{58}(5,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $12$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 58 = 2 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 58.e (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(58, [\chi])\).

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{9} - 26 q^{13} - 14 q^{15} - 2 q^{16} + 2 q^{20} + 14 q^{21} + 4 q^{22} - 16 q^{23} + 12 q^{24} + 22 q^{25} + 14 q^{26} - 4 q^{28} + 18 q^{29} + 16 q^{30} + 28 q^{31} - 10 q^{33} - 4 q^{34} + 4 q^{35} + 18 q^{36} - 28 q^{37} + 22 q^{38} + 28 q^{39} - 14 q^{40} - 4 q^{42} - 28 q^{43} - 28 q^{44} - 4 q^{45} - 14 q^{47} - 8 q^{49} - 28 q^{50} - 4 q^{51} - 2 q^{52} + 30 q^{53} - 32 q^{54} + 28 q^{55} - 20 q^{57} - 10 q^{58} - 48 q^{59} - 14 q^{60} - 28 q^{61} + 10 q^{62} + 22 q^{63} + 2 q^{64} + 2 q^{65} - 16 q^{67} - 14 q^{68} - 28 q^{69} + 30 q^{71} + 42 q^{73} + 2 q^{74} + 28 q^{76} + 14 q^{77} - 16 q^{78} + 28 q^{79} - 2 q^{80} + 26 q^{81} - 20 q^{82} + 28 q^{85} + 52 q^{86} + 4 q^{87} - 4 q^{88} + 14 q^{89} + 70 q^{90} - 4 q^{91} + 16 q^{92} + 66 q^{93} - 8 q^{94} + 2 q^{96} - 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(58, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
58.2.e.a 58.e 29.e $12$ $0.463$ \(\Q(\zeta_{28})\) None 58.2.e.a \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{14}]$ \(q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(58, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(58, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)