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 $0$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
228.3.h.a \(6\) \(6.213\) 6.0.219615408.1 None \(0\) \(0\) \(-2\) \(-2\) \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-3q^{9}+(-4+\cdots)q^{11}+\cdots\)

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

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