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Properties

Label 228.2.p
Level $228$
Weight $2$
Character orbit 228.p
Rep. character $\chi_{228}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $4$
Sturm bound $80$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 92 12 80
Cusp forms 68 12 56
Eisenstein series 24 0 24

Trace form

\( 12 q - 3 q^{3} - 4 q^{7} + q^{9} + O(q^{10}) \) \( 12 q - 3 q^{3} - 4 q^{7} + q^{9} + 6 q^{13} - 21 q^{15} + 16 q^{19} + 8 q^{25} - 30 q^{33} + 18 q^{39} + 24 q^{43} - 34 q^{45} + 36 q^{49} - 9 q^{51} - 4 q^{55} - 15 q^{57} + 2 q^{61} + 2 q^{63} - 60 q^{67} - 42 q^{73} + 12 q^{79} - 11 q^{81} - 34 q^{85} + 18 q^{87} + 54 q^{91} + 30 q^{93} - 18 q^{97} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a 228.p 57.f $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-10\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}-5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
228.2.p.b 228.p 57.f $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(2\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+q^{7}+3\zeta_{6}q^{9}+(2-\zeta_{6})q^{13}+\cdots\)
228.2.p.c 228.p 57.f $4$ $1.821$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-2\) \(9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
228.2.p.d 228.p 57.f $4$ $1.821$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{3}+(-3+2\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(228, [\chi]) \cong \)