Properties

Label 528.2.b
Level $528$
Weight $2$
Character orbit 528.b
Rep. character $\chi_{528}(65,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $6$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q + 2 q^{3} + 2 q^{9} + O(q^{10}) \) \( 22 q + 2 q^{3} + 2 q^{9} + 2 q^{15} - 10 q^{25} + 8 q^{27} + 4 q^{31} - 2 q^{33} - 4 q^{37} + 8 q^{45} - 6 q^{49} - 4 q^{55} + 60 q^{67} - 12 q^{69} + 4 q^{75} - 6 q^{81} - 48 q^{91} - 24 q^{93} - 20 q^{97} - 22 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
528.2.b.a \(2\) \(4.216\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(0\) \(0\) \(q-\beta q^{3}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
528.2.b.b \(2\) \(4.216\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}-\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.c \(2\) \(4.216\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}-\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.d \(4\) \(4.216\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
528.2.b.e \(6\) \(4.216\) 6.0.7388168.1 None \(0\) \(-1\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
528.2.b.f \(6\) \(4.216\) 6.0.7388168.1 None \(0\) \(-1\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)