Properties

Label 2880.2.o
Level $2880$
Weight $2$
Character orbit 2880.o
Rep. character $\chi_{2880}(2879,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $49$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(49\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 624 48 576
Cusp forms 528 48 480
Eisenstein series 96 0 96

Trace form

\( 48q + O(q^{10}) \) \( 48q + 48q^{49} + 32q^{61} + O(q^{100}) \)

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.o.a \(4\) \(22.997\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}-2\zeta_{8}q^{13}-5\zeta_{8}^{3}q^{17}+\cdots\)
2880.2.o.b \(4\) \(22.997\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}q^{13}+(-\zeta_{8}^{2}+2\zeta_{8}^{3})q^{17}+\cdots\)
2880.2.o.c \(8\) \(22.997\) 8.0.3317760000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{4}q^{7}-\beta _{7}q^{11}+\beta _{5}q^{13}+\cdots\)
2880.2.o.d \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{2})q^{5}-\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
2880.2.o.e \(12\) \(22.997\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)
2880.2.o.f \(12\) \(22.997\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)