Properties

Label 5520.2.be
Level $5520$
Weight $2$
Character orbit 5520.be
Rep. character $\chi_{5520}(1471,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $4$
Sturm bound $2304$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5520.be (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2304\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5520, [\chi])\).

Total New Old
Modular forms 1176 96 1080
Cusp forms 1128 96 1032
Eisenstein series 48 0 48

Trace form

\( 96q - 96q^{9} + O(q^{10}) \) \( 96q - 96q^{9} - 96q^{25} + 48q^{41} + 144q^{49} + 96q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5520, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5520.2.be.a \(16\) \(44.077\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{10}q^{3}+\beta _{10}q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
5520.2.be.b \(16\) \(44.077\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{10}q^{3}+\beta _{10}q^{5}+(1+\beta _{4})q^{7}-q^{9}+\cdots\)
5520.2.be.c \(32\) \(44.077\) None \(0\) \(0\) \(0\) \(-8\)
5520.2.be.d \(32\) \(44.077\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(5520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1104, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1840, [\chi])\)\(^{\oplus 2}\)