Properties

Label 2880.2.bj
Level $2880$
Weight $2$
Character orbit 2880.bj
Rep. character $\chi_{2880}(737,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(19\), \(23\)

Dimensions

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

Total New Old
Modular forms 1248 96 1152
Cusp forms 1056 96 960
Eisenstein series 192 0 192

Trace form

\( 96q + O(q^{10}) \) \( 96q + 192q^{97} + O(q^{100}) \)

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.bj.a \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1-\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2880.2.bj.b \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1-\zeta_{24}^{2}-\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2880.2.bj.c \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1+\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2880.2.bj.d \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1+\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
2880.2.bj.e \(32\) \(22.997\) None \(0\) \(0\) \(0\) \(0\)
2880.2.bj.f \(32\) \(22.997\) None \(0\) \(0\) \(0\) \(0\)

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

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