Properties

Label 2880.2.t
Level $2880$
Weight $2$
Character orbit 2880.t
Rep. character $\chi_{2880}(721,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $5$
Sturm bound $1152$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(1152\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1216 80 1136
Cusp forms 1088 80 1008
Eisenstein series 128 0 128

Trace form

\( 80q + O(q^{10}) \) \( 80q + 8q^{11} - 8q^{19} - 16q^{29} - 16q^{37} - 8q^{43} - 40q^{47} - 80q^{49} + 16q^{53} - 40q^{59} - 16q^{61} - 8q^{67} + 16q^{77} + 16q^{79} + 40q^{83} + 16q^{85} + 64q^{91} + 32q^{95} + O(q^{100}) \)

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.t.a \(4\) \(22.997\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{7}+\cdots\)
2880.2.t.b \(8\) \(22.997\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
2880.2.t.c \(16\) \(22.997\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{5}+(-\beta _{1}+\beta _{4}+\beta _{7}-\beta _{8}-\beta _{10}+\cdots)q^{7}+\cdots\)
2880.2.t.d \(20\) \(22.997\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{5}-\beta _{13}q^{7}+(-\beta _{5}+\beta _{8})q^{11}+\cdots\)
2880.2.t.e \(32\) \(22.997\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)