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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
114.2.h.a \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.b \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(6\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.c \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-6\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.d \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-4\) \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.e \(4\) \(0.910\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(0\) \(8\) \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
114.2.h.f \(4\) \(0.910\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(0\) \(8\) \(q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)

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

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