Properties

Label 5400.2.f
Level $5400$
Weight $2$
Character orbit 5400.f
Rep. character $\chi_{5400}(649,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $32$
Sturm bound $2160$
Trace bound $29$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5400.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 32 \)
Sturm bound: \(2160\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5400, [\chi])\).

Total New Old
Modular forms 1152 72 1080
Cusp forms 1008 72 936
Eisenstein series 144 0 144

Trace form

\( 72q + O(q^{10}) \) \( 72q + 4q^{31} - 84q^{49} - 48q^{61} - 52q^{79} - 68q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5400.2.f.a \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-6q^{11}-6iq^{13}-2iq^{17}+\cdots\)
5400.2.f.b \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-5q^{11}-4iq^{13}+8iq^{17}+\cdots\)
5400.2.f.c \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-5q^{11}-iq^{13}+2iq^{17}+\cdots\)
5400.2.f.d \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\)
5400.2.f.e \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-4q^{11}+iq^{13}-4iq^{17}+\cdots\)
5400.2.f.f \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-4q^{11}+2iq^{13}-5iq^{17}+\cdots\)
5400.2.f.g \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{7}-4q^{11}+iq^{13}+8iq^{17}+\cdots\)
5400.2.f.h \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-3q^{11}-3iq^{13}-2iq^{17}+\cdots\)
5400.2.f.i \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}-2iq^{13}-2iq^{17}+\cdots\)
5400.2.f.j \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots\)
5400.2.f.k \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}-5iq^{13}+4iq^{17}+\cdots\)
5400.2.f.l \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{7}-2q^{11}+4iq^{13}+iq^{17}+\cdots\)
5400.2.f.m \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-q^{11}-iq^{13}+iq^{17}-4q^{19}+\cdots\)
5400.2.f.n \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-6iq^{13}-7iq^{17}-7q^{19}+\cdots\)
5400.2.f.o \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-6iq^{13}+7iq^{17}-7q^{19}+\cdots\)
5400.2.f.p \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+q^{11}-iq^{13}-iq^{17}-4q^{19}+\cdots\)
5400.2.f.q \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-2iq^{13}+2iq^{17}+\cdots\)
5400.2.f.r \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots\)
5400.2.f.s \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{7}+2q^{11}+4iq^{13}-iq^{17}+\cdots\)
5400.2.f.t \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-5iq^{13}-4iq^{17}+\cdots\)
5400.2.f.u \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+3q^{11}-3iq^{13}+2iq^{17}+\cdots\)
5400.2.f.v \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+4q^{11}+iq^{13}+4iq^{17}+\cdots\)
5400.2.f.w \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+4q^{11}+6iq^{13}-6iq^{17}+\cdots\)
5400.2.f.x \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}+2iq^{13}+5iq^{17}+\cdots\)
5400.2.f.y \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{7}+4q^{11}+iq^{13}-8iq^{17}+\cdots\)
5400.2.f.z \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+5q^{11}-4iq^{13}-8iq^{17}+\cdots\)
5400.2.f.ba \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+5q^{11}-iq^{13}-2iq^{17}+\cdots\)
5400.2.f.bb \(2\) \(43.119\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+6q^{11}-6iq^{13}+2iq^{17}+\cdots\)
5400.2.f.bc \(4\) \(43.119\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{7}-q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5400.2.f.bd \(4\) \(43.119\) \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}-\beta _{3}q^{11}+3\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.be \(4\) \(43.119\) \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}+\beta _{3}q^{11}+3\beta _{2}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.bf \(4\) \(43.119\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{7}+q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)