Properties

Label 588.2.b
Level $588$
Weight $2$
Character orbit 588.b
Rep. character $\chi_{588}(391,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $4$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

Trace form

\( 40q + 4q^{2} - 4q^{4} + 16q^{8} + 40q^{9} + O(q^{10}) \) \( 40q + 4q^{2} - 4q^{4} + 16q^{8} + 40q^{9} + 12q^{16} + 4q^{18} - 12q^{22} - 32q^{25} + 32q^{29} - 16q^{30} - 16q^{32} - 4q^{36} + 40q^{37} - 40q^{44} + 24q^{46} - 52q^{50} - 48q^{53} + 24q^{57} + 4q^{58} - 4q^{60} - 4q^{64} - 16q^{65} + 16q^{72} + 12q^{74} + 36q^{78} + 40q^{81} - 32q^{85} - 36q^{86} + 100q^{88} - 56q^{92} + 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
588.2.b.a \(8\) \(4.695\) 8.0.562828176.1 None \(-2\) \(-8\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
588.2.b.b \(8\) \(4.695\) 8.0.562828176.1 None \(-2\) \(8\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.b.c \(12\) \(4.695\) 12.0.\(\cdots\).1 None \(4\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
588.2.b.d \(12\) \(4.695\) 12.0.\(\cdots\).1 None \(4\) \(12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)