Properties

Label 5850.2.e
Level $5850$
Weight $2$
Character orbit 5850.e
Rep. character $\chi_{5850}(5149,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $39$
Sturm bound $2520$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5850.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 39 \)
Sturm bound: \(2520\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5850, [\chi])\).

Total New Old
Modular forms 1308 90 1218
Cusp forms 1212 90 1122
Eisenstein series 96 0 96

Trace form

\( 90 q - 90 q^{4} + O(q^{10}) \) \( 90 q - 90 q^{4} - 4 q^{11} + 8 q^{14} + 90 q^{16} + 4 q^{19} + 6 q^{26} + 8 q^{34} + 24 q^{41} + 4 q^{44} + 32 q^{46} - 114 q^{49} - 8 q^{56} - 32 q^{59} + 32 q^{61} - 90 q^{64} + 80 q^{71} - 4 q^{76} - 8 q^{79} + 56 q^{86} - 48 q^{89} - 20 q^{91} - 40 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5850, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5850.2.e.a 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-6q^{11}+\cdots\)
5850.2.e.b 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-6q^{11}+\cdots\)
5850.2.e.c 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-4q^{11}+\cdots\)
5850.2.e.d 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-4q^{11}+\cdots\)
5850.2.e.e 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{8}-4q^{11}-iq^{13}+\cdots\)
5850.2.e.f 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}-4q^{11}+iq^{13}+\cdots\)
5850.2.e.g 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.h 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.i 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.j 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-3q^{11}+\cdots\)
5850.2.e.k 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-2q^{11}+\cdots\)
5850.2.e.l 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-q^{11}+\cdots\)
5850.2.e.m 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+iq^{13}+\cdots\)
5850.2.e.n 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+iq^{13}+\cdots\)
5850.2.e.o 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-iq^{13}+\cdots\)
5850.2.e.p 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+iq^{13}+q^{16}+\cdots\)
5850.2.e.q 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{8}-iq^{13}+q^{16}+\cdots\)
5850.2.e.r 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-iq^{13}+\cdots\)
5850.2.e.s 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+iq^{13}+\cdots\)
5850.2.e.t 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+iq^{13}+\cdots\)
5850.2.e.u 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+2q^{11}+\cdots\)
5850.2.e.v 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots\)
5850.2.e.w 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+2q^{11}+\cdots\)
5850.2.e.x 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+3q^{11}+\cdots\)
5850.2.e.y 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+3q^{11}+iq^{13}+\cdots\)
5850.2.e.z 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}+3q^{11}+\cdots\)
5850.2.e.ba 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+5iq^{7}+iq^{8}+3q^{11}+\cdots\)
5850.2.e.bb 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+4q^{11}+\cdots\)
5850.2.e.bc 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+4q^{11}+\cdots\)
5850.2.e.bd 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+4q^{11}+\cdots\)
5850.2.e.be 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+5q^{11}+\cdots\)
5850.2.e.bf 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+6q^{11}+\cdots\)
5850.2.e.bg 5850.e 5.b $2$ $46.712$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+6q^{11}+\cdots\)
5850.2.e.bh 5850.e 5.b $4$ $46.712$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{8}+\cdots\)
5850.2.e.bi 5850.e 5.b $4$ $46.712$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{7}-\beta _{2}q^{8}+\cdots\)
5850.2.e.bj 5850.e 5.b $4$ $46.712$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{8}+\cdots\)
5850.2.e.bk 5850.e 5.b $4$ $46.712$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{2}-q^{4}+\zeta_{8}^{2}q^{7}+\zeta_{8}q^{8}+2\zeta_{8}^{3}q^{11}+\cdots\)
5850.2.e.bl 5850.e 5.b $4$ $46.712$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{8}+\cdots\)
5850.2.e.bm 5850.e 5.b $4$ $46.712$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{7}+\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2925, [\chi])\)\(^{\oplus 2}\)