Properties

Label 114.2.b
Level $114$
Weight $2$
Character orbit 114.b
Rep. character $\chi_{114}(113,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(29\)

Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

Trace form

\( 8q + 8q^{4} - 2q^{6} - 12q^{7} + 2q^{9} + O(q^{10}) \) \( 8q + 8q^{4} - 2q^{6} - 12q^{7} + 2q^{9} + 8q^{16} - 12q^{19} - 2q^{24} - 16q^{25} - 12q^{28} - 4q^{30} + 2q^{36} - 18q^{39} - 22q^{42} + 16q^{43} + 52q^{45} + 12q^{49} - 20q^{54} + 16q^{55} + 18q^{57} + 12q^{58} - 24q^{61} + 22q^{63} + 8q^{64} + 44q^{66} + 28q^{73} - 12q^{76} - 46q^{81} - 8q^{85} - 78q^{87} + 12q^{93} - 2q^{96} + 28q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.910\) \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(0\) \(-8\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
114.2.b.b \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(0\) \(2\) \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.c \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(2\) \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.d \(2\) \(0.910\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(-8\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)

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

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