Properties

Label 4560.2.d
Level $4560$
Weight $2$
Character orbit 4560.d
Rep. character $\chi_{4560}(2431,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $12$
Sturm bound $1920$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1920\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4560, [\chi])\).

Total New Old
Modular forms 984 80 904
Cusp forms 936 80 856
Eisenstein series 48 0 48

Trace form

\( 80q + 80q^{9} + O(q^{10}) \) \( 80q + 80q^{9} + 80q^{25} - 112q^{49} - 8q^{57} - 112q^{61} - 16q^{73} + 96q^{77} + 80q^{81} - 16q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4560, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4560.2.d.a \(2\) \(36.412\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}-q^{5}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
4560.2.d.b \(2\) \(36.412\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+q^{5}+q^{9}-2\zeta_{6}q^{11}-q^{15}+\cdots\)
4560.2.d.c \(2\) \(36.412\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}-q^{5}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
4560.2.d.d \(2\) \(36.412\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+q^{5}+q^{9}+2\zeta_{6}q^{11}+q^{15}+\cdots\)
4560.2.d.e \(6\) \(36.412\) 6.0.9821011968.3 None \(0\) \(-6\) \(-6\) \(0\) \(q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
4560.2.d.f \(6\) \(36.412\) 6.0.792772608.2 None \(0\) \(-6\) \(6\) \(0\) \(q-q^{3}+q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
4560.2.d.g \(6\) \(36.412\) 6.0.9821011968.3 None \(0\) \(6\) \(-6\) \(0\) \(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
4560.2.d.h \(6\) \(36.412\) 6.0.792772608.2 None \(0\) \(6\) \(6\) \(0\) \(q+q^{3}+q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
4560.2.d.i \(12\) \(36.412\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-12\) \(0\) \(q-q^{3}-q^{5}+\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)
4560.2.d.j \(12\) \(36.412\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-12\) \(12\) \(0\) \(q-q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+\beta _{6}q^{11}+\cdots\)
4560.2.d.k \(12\) \(36.412\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(-12\) \(0\) \(q+q^{3}-q^{5}+\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)
4560.2.d.l \(12\) \(36.412\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(12\) \(12\) \(0\) \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+\beta _{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1520, [\chi])\)\(^{\oplus 2}\)