Properties

Label 2880.2.h
Level $2880$
Weight $2$
Character orbit 2880.h
Rep. character $\chi_{2880}(1151,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(7\), \(11\), \(23\)

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

\( 32q + O(q^{10}) \) \( 32q + 32q^{13} - 32q^{25} - 32q^{37} - 32q^{49} - 64q^{61} + 32q^{85} + O(q^{100}) \)

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.h.a \(4\) \(22.997\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(-4-\zeta_{8}^{3})q^{11}+\cdots\)
2880.2.h.b \(4\) \(22.997\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+\zeta_{8}^{3}q^{11}+\cdots\)
2880.2.h.c \(4\) \(22.997\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
2880.2.h.d \(4\) \(22.997\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(4+\zeta_{8}^{3})q^{11}+\cdots\)
2880.2.h.e \(8\) \(22.997\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{5}-\beta _{7}q^{7}+\beta _{1}q^{11}+(-2-\beta _{2}+\cdots)q^{13}+\cdots\)
2880.2.h.f \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{5}+\zeta_{24}^{5}q^{7}+(\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)