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Properties

Label 228.3.h
Level $228$
Weight $3$
Character orbit 228.h
Rep. character $\chi_{228}(37,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 228.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).

Total New Old
Modular forms 86 6 80
Cusp forms 74 6 68
Eisenstein series 12 0 12

Trace form

\( 6 q - 2 q^{5} - 2 q^{7} - 18 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{5} - 2 q^{7} - 18 q^{9} - 26 q^{11} - 50 q^{17} - 10 q^{19} + 28 q^{23} + 28 q^{25} + 2 q^{35} + 72 q^{39} - 210 q^{43} + 6 q^{45} + 22 q^{47} - 36 q^{49} + 10 q^{55} + 48 q^{57} + 214 q^{61} + 6 q^{63} + 102 q^{73} + 266 q^{77} + 54 q^{81} - 404 q^{83} + 370 q^{85} - 144 q^{87} - 120 q^{93} + 358 q^{95} + 78 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.3.h.a 228.h 19.b $6$ $6.213$ 6.0.219615408.1 None \(0\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-3q^{9}+(-4+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)