Properties

Label 2880.2.f
Level $2880$
Weight $2$
Character orbit 2880.f
Rep. character $\chi_{2880}(1729,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $24$
Sturm bound $1152$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(1152\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

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

Total New Old
Modular forms 624 62 562
Cusp forms 528 58 470
Eisenstein series 96 4 92

Trace form

\( 58q - 2q^{5} + O(q^{10}) \) \( 58q - 2q^{5} + 2q^{25} - 4q^{29} - 4q^{41} - 50q^{49} - 12q^{61} - 32q^{85} + 12q^{89} + O(q^{100}) \)

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.f.a \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}+2iq^{7}-6q^{11}-2iq^{13}+\cdots\)
2880.2.f.b \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)
2880.2.f.c \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+2iq^{7}-2q^{11}-6iq^{13}+\cdots\)
2880.2.f.d \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+4iq^{13}-2iq^{17}+\cdots\)
2880.2.f.e \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}+2iq^{7}+2q^{11}+6iq^{13}+\cdots\)
2880.2.f.f \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}+4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
2880.2.f.g \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+2iq^{7}+6q^{11}+2iq^{13}+\cdots\)
2880.2.f.h \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots\)
2880.2.f.i \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{7}+4q^{11}-2iq^{13}+\cdots\)
2880.2.f.j \(2\) \(22.997\) \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+2\beta q^{17}-4q^{19}+4\beta q^{23}+\cdots\)
2880.2.f.k \(2\) \(22.997\) \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+2\beta q^{17}+4q^{19}-4\beta q^{23}+\cdots\)
2880.2.f.l \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-i)q^{5}+2iq^{7}-4q^{11}-2iq^{17}+\cdots\)
2880.2.f.m \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-i)q^{5}+2iq^{7}-2iq^{13}-8q^{19}+\cdots\)
2880.2.f.n \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1-i)q^{5}+2iq^{13}-4iq^{17}+(-3+\cdots)q^{25}+\cdots\)
2880.2.f.o \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+2iq^{7}+2iq^{13}+8q^{19}+\cdots\)
2880.2.f.p \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+2iq^{7}+4q^{11}+2iq^{17}+\cdots\)
2880.2.f.q \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots\)
2880.2.f.r \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
2880.2.f.s \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}-4iq^{13}-2iq^{17}+(3+\cdots)q^{25}+\cdots\)
2880.2.f.t \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}+2iq^{7}+2q^{11}-2iq^{13}+\cdots\)
2880.2.f.u \(2\) \(22.997\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}+4iq^{7}+4q^{11}+4iq^{13}+\cdots\)
2880.2.f.v \(4\) \(22.997\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots\)
2880.2.f.w \(4\) \(22.997\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots\)
2880.2.f.x \(8\) \(22.997\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)