Properties

Label 4600.2.e
Level $4600$
Weight $2$
Character orbit 4600.e
Rep. character $\chi_{4600}(4049,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $23$
Sturm bound $1440$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(1440\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4600, [\chi])\).

Total New Old
Modular forms 744 100 644
Cusp forms 696 100 596
Eisenstein series 48 0 48

Trace form

\( 100 q - 104 q^{9} + O(q^{10}) \) \( 100 q - 104 q^{9} - 16 q^{29} + 8 q^{31} - 48 q^{39} + 20 q^{41} - 84 q^{49} + 84 q^{51} + 24 q^{59} - 20 q^{61} - 8 q^{69} + 40 q^{71} + 8 q^{79} + 116 q^{81} + 12 q^{89} - 24 q^{91} - 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4600.2.e.a 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+2iq^{7}-6q^{9}-5iq^{13}+\cdots\)
4600.2.e.b 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-iq^{13}+6q^{21}+\cdots\)
4600.2.e.c 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots\)
4600.2.e.d 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-5iq^{13}+\cdots\)
4600.2.e.e 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}-4q^{11}+5iq^{13}+\cdots\)
4600.2.e.f 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-4iq^{7}+2q^{9}-2q^{11}-7iq^{13}+\cdots\)
4600.2.e.g 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}+iq^{13}+4iq^{17}+\cdots\)
4600.2.e.h 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{9}+2q^{11}+5iq^{13}-4iq^{17}+\cdots\)
4600.2.e.i 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-4iq^{7}+2q^{9}+3q^{11}-2iq^{13}+\cdots\)
4600.2.e.j 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}-6q^{11}+2iq^{13}-3iq^{17}+\cdots\)
4600.2.e.k 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}+3q^{9}+6q^{11}+2iq^{13}+\cdots\)
4600.2.e.l 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
4600.2.e.m 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.n 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.o 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{9}+(2-2\beta _{3})q^{11}+\cdots\)
4600.2.e.p 4600.e 5.b $6$ $36.731$ 6.0.431642176.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-3+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.q 4600.e 5.b $6$ $36.731$ 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{3}+(-2\beta _{3}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4600.2.e.r 4600.e 5.b $6$ $36.731$ 6.0.24681024.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.s 4600.e 5.b $6$ $36.731$ 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{5})q^{3}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots\)
4600.2.e.t 4600.e 5.b $8$ $36.731$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{7})q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots\)
4600.2.e.u 4600.e 5.b $10$ $36.731$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{6}+\beta _{8})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.v 4600.e 5.b $10$ $36.731$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{5})q^{3}+\beta _{8}q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.w 4600.e 5.b $10$ $36.731$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{6})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2300, [\chi])\)\(^{\oplus 2}\)