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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5850.2.e.a \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-6q^{11}+\cdots\)
5850.2.e.b \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-6q^{11}+\cdots\)
5850.2.e.c \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-4q^{11}+\cdots\)
5850.2.e.d \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-4q^{11}+\cdots\)
5850.2.e.e \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-4q^{11}-iq^{13}+\cdots\)
5850.2.e.f \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}-4q^{11}+iq^{13}+\cdots\)
5850.2.e.g \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.h \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.i \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-4q^{11}+\cdots\)
5850.2.e.j \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-3q^{11}+\cdots\)
5850.2.e.k \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-2q^{11}+\cdots\)
5850.2.e.l \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-q^{11}+\cdots\)
5850.2.e.m \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+iq^{13}+\cdots\)
5850.2.e.n \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+iq^{13}+\cdots\)
5850.2.e.o \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-iq^{13}+\cdots\)
5850.2.e.p \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+iq^{13}+q^{16}+\cdots\)
5850.2.e.q \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-iq^{13}+q^{16}+\cdots\)
5850.2.e.r \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-iq^{13}+\cdots\)
5850.2.e.s \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+iq^{13}+\cdots\)
5850.2.e.t \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+iq^{13}+\cdots\)
5850.2.e.u \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+2q^{11}+\cdots\)
5850.2.e.v \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots\)
5850.2.e.w \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+2q^{11}+\cdots\)
5850.2.e.x \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+3q^{11}+\cdots\)
5850.2.e.y \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{11}+iq^{13}+\cdots\)
5850.2.e.z \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}+3q^{11}+\cdots\)
5850.2.e.ba \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+5iq^{7}+iq^{8}+3q^{11}+\cdots\)
5850.2.e.bb \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+4q^{11}+\cdots\)
5850.2.e.bc \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+4q^{11}+\cdots\)
5850.2.e.bd \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+4q^{11}+\cdots\)
5850.2.e.be \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+5q^{11}+\cdots\)
5850.2.e.bf \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+6q^{11}+\cdots\)
5850.2.e.bg \(2\) \(46.712\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+6q^{11}+\cdots\)
5850.2.e.bh \(4\) \(46.712\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{8}+\cdots\)
5850.2.e.bi \(4\) \(46.712\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{7}-\beta _{2}q^{8}+\cdots\)
5850.2.e.bj \(4\) \(46.712\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{8}+\cdots\)
5850.2.e.bk \(4\) \(46.712\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-q^{4}+\zeta_{8}^{2}q^{7}+\zeta_{8}q^{8}+2\zeta_{8}^{3}q^{11}+\cdots\)
5850.2.e.bl \(4\) \(46.712\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{8}+\cdots\)
5850.2.e.bm \(4\) \(46.712\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{7}+\beta _{1}q^{8}+\cdots\)

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

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