Properties

Label 5700.2.f
Level $5700$
Weight $2$
Character orbit 5700.f
Rep. character $\chi_{5700}(3649,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $18$
Sturm bound $2400$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5700.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(2400\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5700, [\chi])\).

Total New Old
Modular forms 1236 56 1180
Cusp forms 1164 56 1108
Eisenstein series 72 0 72

Trace form

\( 56 q - 56 q^{9} + O(q^{10}) \) \( 56 q - 56 q^{9} - 4 q^{11} - 4 q^{19} - 40 q^{29} + 8 q^{31} + 16 q^{39} + 16 q^{41} - 108 q^{49} + 16 q^{51} - 32 q^{59} + 76 q^{61} - 16 q^{69} + 32 q^{71} - 8 q^{79} + 56 q^{81} - 8 q^{89} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5700.2.f.a 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-5q^{11}+6iq^{13}+\cdots\)
5700.2.f.b 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4q^{11}-4iq^{17}+\cdots\)
5700.2.f.c 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4q^{11}+6iq^{17}+\cdots\)
5700.2.f.d 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-2iq^{13}+\cdots\)
5700.2.f.e 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4iq^{13}-q^{19}+\cdots\)
5700.2.f.f 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{7}-q^{9}+4iq^{13}+6iq^{17}+\cdots\)
5700.2.f.g 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}-q^{9}-4iq^{13}+2iq^{17}+\cdots\)
5700.2.f.h 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+iq^{7}-q^{9}-2iq^{17}+q^{19}+\cdots\)
5700.2.f.i 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}+2q^{11}+6iq^{13}+\cdots\)
5700.2.f.j 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+5iq^{7}-q^{9}+2q^{11}-2iq^{13}+\cdots\)
5700.2.f.k 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}+2q^{11}+2iq^{13}-6iq^{17}+\cdots\)
5700.2.f.l 5700.f 5.b $2$ $45.515$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{7}-q^{9}+4q^{11}+2iq^{17}+\cdots\)
5700.2.f.m 5700.f 5.b $4$ $45.515$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(-1-\beta _{3})q^{11}+\cdots\)
5700.2.f.n 5700.f 5.b $4$ $45.515$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
5700.2.f.o 5700.f 5.b $4$ $45.515$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+4\beta _{1}q^{7}-q^{9}+(1+\beta _{3})q^{11}+\cdots\)
5700.2.f.p 5700.f 5.b $6$ $45.515$ 6.0.37161216.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{5}q^{7}-q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
5700.2.f.q 5700.f 5.b $6$ $45.515$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(\beta _{1}-\beta _{4})q^{7}-q^{9}+(2-\beta _{2}+\cdots)q^{11}+\cdots\)
5700.2.f.r 5700.f 5.b $8$ $45.515$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{5})q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2850, [\chi])\)\(^{\oplus 2}\)