Properties

Label 4800.2.f
Level $4800$
Weight $2$
Character orbit 4800.f
Rep. character $\chi_{4800}(3649,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $36$
Sturm bound $1920$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4800.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(1920\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4800, [\chi])\).

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \) \( 72 q - 72 q^{9} - 16 q^{41} - 72 q^{49} + 32 q^{61} - 32 q^{69} + 72 q^{81} - 16 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4800.2.f.a 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots\)
4800.2.f.b 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots\)
4800.2.f.c 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots\)
4800.2.f.d 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots\)
4800.2.f.e 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
4800.2.f.f 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots\)
4800.2.f.g 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots\)
4800.2.f.h 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots\)
4800.2.f.i 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}-4q^{11}+6iq^{13}-6iq^{17}+\cdots\)
4800.2.f.j 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}-4q^{11}-2iq^{13}+2iq^{17}+\cdots\)
4800.2.f.k 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots\)
4800.2.f.l 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots\)
4800.2.f.m 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots\)
4800.2.f.n 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}+6iq^{13}+2iq^{17}+\cdots\)
4800.2.f.o 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}-2iq^{13}-6iq^{17}-4q^{19}+\cdots\)
4800.2.f.p 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots\)
4800.2.f.q 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots\)
4800.2.f.r 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots\)
4800.2.f.s 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots\)
4800.2.f.t 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots\)
4800.2.f.u 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}-6iq^{13}-2iq^{17}+\cdots\)
4800.2.f.v 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+2iq^{13}+6iq^{17}+4q^{19}+\cdots\)
4800.2.f.w 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots\)
4800.2.f.x 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots\)
4800.2.f.y 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+iq^{13}+\cdots\)
4800.2.f.z 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+3iq^{13}+\cdots\)
4800.2.f.ba 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots\)
4800.2.f.bb 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots\)
4800.2.f.bc 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}+4q^{11}-6iq^{13}+6iq^{17}+\cdots\)
4800.2.f.bd 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots\)
4800.2.f.be 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots\)
4800.2.f.bf 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots\)
4800.2.f.bg 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots\)
4800.2.f.bh 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots\)
4800.2.f.bi 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots\)
4800.2.f.bj 4800.f 5.b $2$ $38.328$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)