Properties

Label 114.2.h
Level $114$
Weight $2$
Character orbit 114.h
Rep. character $\chi_{114}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $6$
Sturm bound $40$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(40\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 48 16 32
Cusp forms 32 16 16
Eisenstein series 16 0 16

Trace form

\( 16 q - 3 q^{3} - 8 q^{4} - q^{6} + 12 q^{7} + q^{9} + O(q^{10}) \) \( 16 q - 3 q^{3} - 8 q^{4} - q^{6} + 12 q^{7} + q^{9} - 18 q^{13} + 6 q^{15} - 8 q^{16} - 18 q^{19} - 6 q^{22} - q^{24} + 16 q^{25} - 6 q^{28} + 4 q^{30} - 3 q^{33} + 12 q^{34} + q^{36} - 48 q^{39} + 22 q^{42} + 2 q^{43} - 52 q^{45} + 3 q^{48} - 12 q^{49} + 72 q^{51} + 18 q^{52} + 20 q^{54} - 4 q^{55} + 48 q^{57} - 6 q^{60} - 18 q^{61} - 16 q^{63} + 16 q^{64} + 25 q^{66} + 36 q^{67} - 12 q^{70} + 3 q^{72} + 8 q^{73} + 12 q^{76} + 6 q^{78} - 30 q^{79} - 23 q^{81} - 6 q^{82} + 8 q^{85} - 12 q^{87} - 78 q^{90} - 6 q^{91} - 6 q^{93} + 2 q^{96} + 18 q^{97} + 23 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.2.h.a 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.b 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.c 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.d 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.e 114.h 57.f $4$ $0.910$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
114.2.h.f 114.h 57.f $4$ $0.910$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)

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

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