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Properties

Label 114.3.d
Level $114$
Weight $3$
Character orbit 114.d
Rep. character $\chi_{114}(37,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 114.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(114, [\chi])\).

Total New Old
Modular forms 44 8 36
Cusp forms 36 8 28
Eisenstein series 8 0 8

Trace form

\( 8 q - 16 q^{4} + 4 q^{5} - 12 q^{7} - 24 q^{9} + O(q^{10}) \) \( 8 q - 16 q^{4} + 4 q^{5} - 12 q^{7} - 24 q^{9} + 4 q^{11} + 32 q^{16} + 4 q^{17} - 36 q^{19} - 8 q^{20} - 56 q^{23} + 140 q^{25} - 96 q^{26} + 24 q^{28} - 48 q^{30} + 236 q^{35} + 48 q^{36} + 48 q^{38} - 96 q^{39} + 48 q^{42} + 100 q^{43} - 8 q^{44} - 12 q^{45} - 188 q^{47} - 36 q^{49} + 28 q^{55} + 36 q^{57} + 168 q^{58} - 180 q^{61} - 96 q^{62} + 36 q^{63} - 64 q^{64} + 24 q^{66} - 8 q^{68} - 356 q^{73} - 192 q^{74} + 72 q^{76} + 68 q^{77} + 16 q^{80} + 72 q^{81} + 72 q^{82} + 136 q^{83} + 148 q^{85} - 144 q^{87} + 112 q^{92} + 168 q^{93} - 140 q^{95} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.3.d.a 114.d 19.b $8$ $3.106$ 8.0.\(\cdots\).3 None 114.3.d.a \(0\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-2q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(114, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)