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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
228.2.p.a \(2\) \(1.821\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-10\) \(q+(-1-\zeta_{6})q^{3}-5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
228.2.p.b \(2\) \(1.821\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(2\) \(q+(1+\zeta_{6})q^{3}+q^{7}+3\zeta_{6}q^{9}+(2-\zeta_{6})q^{13}+\cdots\)
228.2.p.c \(4\) \(1.821\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-2\) \(9\) \(2\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
228.2.p.d \(4\) \(1.821\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-9\) \(2\) \(q-\beta _{1}q^{3}+(-3+2\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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