Properties

Label 2880.2.d
Level $2880$
Weight $2$
Character orbit 2880.d
Rep. character $\chi_{2880}(289,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $11$
Sturm bound $1152$
Trace bound $41$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(1152\)
Trace bound: \(41\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(31\), \(41\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

Total New Old
Modular forms 624 60 564
Cusp forms 528 60 468
Eisenstein series 96 0 96

Trace form

\( 60q + O(q^{10}) \) \( 60q + 12q^{25} - 24q^{41} - 60q^{49} - 24q^{65} + 24q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2880.2.d.a \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{7}-iq^{11}+2q^{13}+\cdots\)
2880.2.d.b \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+iq^{7}-iq^{11}+2q^{13}+\cdots\)
2880.2.d.c \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+iq^{7}+iq^{11}-2q^{13}+\cdots\)
2880.2.d.d \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-i)q^{5}+iq^{7}+iq^{11}-2q^{13}+\cdots\)
2880.2.d.e \(4\) \(22.997\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}+2\beta _{3}q^{13}+\cdots\)
2880.2.d.f \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{5}+\zeta_{24}^{5}q^{7}-\zeta_{24}q^{11}+\cdots\)
2880.2.d.g \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\zeta_{24}q^{11}+\cdots\)
2880.2.d.h \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{5}+\zeta_{24}^{5}q^{7}-\zeta_{24}q^{11}+\cdots\)
2880.2.d.i \(8\) \(22.997\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\beta _{1}q^{11}+\cdots\)
2880.2.d.j \(8\) \(22.997\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}-\beta _{1}q^{11}+\cdots\)
2880.2.d.k \(8\) \(22.997\) 8.0.40960000.1 \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{3}q^{7}-\beta _{5}q^{11}+\beta _{6}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)