Properties

Label 228.2.d
Level $228$
Weight $2$
Character orbit 228.d
Rep. character $\chi_{228}(113,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

Total New Old
Modular forms 46 6 40
Cusp forms 34 6 28
Eisenstein series 12 0 12

Trace form

\( 6 q + 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 6 q + 4 q^{7} + 2 q^{9} - 4 q^{19} + 10 q^{25} - 12 q^{39} - 12 q^{43} - 20 q^{45} - 6 q^{49} - 20 q^{55} + 18 q^{57} + 16 q^{61} - 32 q^{63} + 14 q^{81} - 20 q^{85} + 48 q^{93} - 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.2.d.a 228.d 57.d $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(8\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+4q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
228.2.d.b 228.d 57.d $4$ $1.821$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

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