Properties

Label 2880.2.b
Level $2880$
Weight $2$
Character orbit 2880.b
Rep. character $\chi_{2880}(2591,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $4$
Sturm bound $1152$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1152\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(29\)

Dimensions

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

Total New Old
Modular forms 624 32 592
Cusp forms 528 32 496
Eisenstein series 96 0 96

Trace form

\( 32q + O(q^{10}) \) \( 32q + 32q^{25} - 96q^{49} - 64q^{73} + 64q^{97} + O(q^{100}) \)

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.b.a \(8\) \(22.997\) 8.0.40960000.1 None \(0\) \(0\) \(-8\) \(0\) \(q-q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\beta _{2}q^{13}+\cdots\)
2880.2.b.b \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) \(q-q^{5}-\zeta_{24}^{5}q^{7}+\zeta_{24}^{5}q^{11}+\zeta_{24}q^{13}+\cdots\)
2880.2.b.c \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+q^{5}-\zeta_{24}^{6}q^{7}-\zeta_{24}^{6}q^{11}-\zeta_{24}q^{13}+\cdots\)
2880.2.b.d \(8\) \(22.997\) 8.0.40960000.1 None \(0\) \(0\) \(8\) \(0\) \(q+q^{5}+\beta _{3}q^{7}+(\beta _{1}-\beta _{3})q^{11}-\beta _{2}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)