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 $29$

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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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5400.2.f.a 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.s \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-6q^{11}-6iq^{13}-2iq^{17}+\cdots\)
5400.2.f.b 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 216.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}-5q^{11}-4iq^{13}+8iq^{17}+\cdots\)
5400.2.f.c 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-5q^{11}-iq^{13}+2iq^{17}+\cdots\)
5400.2.f.d 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\)
5400.2.f.e 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 216.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}-4q^{11}+iq^{13}-4iq^{17}+\cdots\)
5400.2.f.f 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-4q^{11}+2iq^{13}-5iq^{17}+\cdots\)
5400.2.f.g 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}-4q^{11}+iq^{13}+8iq^{17}+\cdots\)
5400.2.f.h 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-3q^{11}-3iq^{13}-2iq^{17}+\cdots\)
5400.2.f.i 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.t \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-2q^{11}-2iq^{13}-2iq^{17}+\cdots\)
5400.2.f.j 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots\)
5400.2.f.k 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-2q^{11}-5iq^{13}+4iq^{17}+\cdots\)
5400.2.f.l 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}-2q^{11}+4iq^{13}+iq^{17}+\cdots\)
5400.2.f.m 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-q^{11}-iq^{13}+iq^{17}-4q^{19}+\cdots\)
5400.2.f.n 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-6iq^{13}-7iq^{17}-7q^{19}+\cdots\)
5400.2.f.o 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-6iq^{13}+7iq^{17}-7q^{19}+\cdots\)
5400.2.f.p 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+q^{11}-iq^{13}-iq^{17}-4q^{19}+\cdots\)
5400.2.f.q 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.t \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+2q^{11}-2iq^{13}+2iq^{17}+\cdots\)
5400.2.f.r 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots\)
5400.2.f.s 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}+2q^{11}+4iq^{13}-iq^{17}+\cdots\)
5400.2.f.t 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+2q^{11}-5iq^{13}-4iq^{17}+\cdots\)
5400.2.f.u 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{11}-3iq^{13}+2iq^{17}+\cdots\)
5400.2.f.v 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 216.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}+4q^{11}+iq^{13}+4iq^{17}+\cdots\)
5400.2.f.w 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}+4q^{11}+6iq^{13}-6iq^{17}+\cdots\)
5400.2.f.x 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 1080.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+4q^{11}+2iq^{13}+5iq^{17}+\cdots\)
5400.2.f.y 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}+4q^{11}+iq^{13}-8iq^{17}+\cdots\)
5400.2.f.z 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 216.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{7}+5q^{11}-4iq^{13}-8iq^{17}+\cdots\)
5400.2.f.ba 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+5q^{11}-iq^{13}-2iq^{17}+\cdots\)
5400.2.f.bb 5400.f 5.b $2$ $43.119$ \(\Q(\sqrt{-1}) \) None 5400.2.a.s \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+6q^{11}-6iq^{13}+2iq^{17}+\cdots\)
5400.2.f.bc 5400.f 5.b $4$ $43.119$ \(\Q(i, \sqrt{13})\) None 5400.2.a.bx \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{7}-q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5400.2.f.bd 5400.f 5.b $4$ $43.119$ \(\Q(i, \sqrt{73})\) None 1080.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{7}-\beta _{3}q^{11}+3\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.be 5400.f 5.b $4$ $43.119$ \(\Q(i, \sqrt{73})\) None 1080.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{7}+\beta _{3}q^{11}+3\beta _{2}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.bf 5400.f 5.b $4$ $43.119$ \(\Q(i, \sqrt{13})\) None 5400.2.a.bx \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{7}+q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)

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

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