Properties

Label 114.2.l
Level $114$
Weight $2$
Character orbit 114.l
Rep. character $\chi_{114}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $36$
Newform subspaces $2$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(114, [\chi])\).

Total New Old
Modular forms 144 36 108
Cusp forms 96 36 60
Eisenstein series 48 0 48

Trace form

\( 36 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{3} + 3 q^{6} - 3 q^{9} - 24 q^{13} - 6 q^{15} - 12 q^{19} - 48 q^{22} + 3 q^{24} - 36 q^{25} - 9 q^{27} + 12 q^{28} - 51 q^{33} - 12 q^{34} - 3 q^{36} + 12 q^{39} - 12 q^{43} + 36 q^{46} + 6 q^{48} + 42 q^{49} + 9 q^{51} - 12 q^{52} + 54 q^{54} + 60 q^{55} + 24 q^{57} + 24 q^{58} + 42 q^{60} + 108 q^{61} + 66 q^{63} - 18 q^{64} + 3 q^{66} - 30 q^{67} + 54 q^{69} + 48 q^{70} + 6 q^{72} - 84 q^{73} - 42 q^{78} - 12 q^{79} - 3 q^{81} + 6 q^{82} - 54 q^{84} - 54 q^{87} - 12 q^{90} - 36 q^{91} - 150 q^{93} + 18 q^{97} - 132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.2.l.a 114.l 57.j $18$ $0.910$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 114.2.l.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
114.2.l.b 114.l 57.j $18$ $0.910$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 114.2.l.a \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(114, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)