Properties

Label 3850.2.c
Level $3850$
Weight $2$
Character orbit 3850.c
Rep. character $\chi_{3850}(1849,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $29$
Sturm bound $1440$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(1440\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(3\), \(13\), \(17\), \(19\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 744 92 652
Cusp forms 696 92 604
Eisenstein series 48 0 48

Trace form

\( 92 q - 92 q^{4} - 108 q^{9} + 4 q^{11} - 8 q^{14} + 92 q^{16} + 24 q^{26} - 40 q^{29} + 24 q^{31} - 40 q^{34} + 108 q^{36} + 48 q^{39} - 40 q^{41} - 4 q^{44} - 92 q^{49} + 16 q^{51} + 8 q^{56} + 88 q^{59}+ \cdots - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3850.2.c.a 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.b 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.c 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-i q^{7}+\cdots\)
3850.2.c.d 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 154.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.e 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.f 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
3850.2.c.g 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
3850.2.c.h 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{4}+i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.i 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}-q^{4}-i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.j 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 154.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}-q^{4}-i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.k 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}-q^{4}+i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.l 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 154.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.m 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.n 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 3850.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}+i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\)
3850.2.c.o 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}+i q^{7}+\cdots\)
3850.2.c.p 3850.c 5.b $2$ $30.742$ \(\Q(\sqrt{-1}) \) None 770.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-i q^{7}+\cdots\)
3850.2.c.q 3850.c 5.b $4$ $30.742$ \(\Q(i, \sqrt{5})\) None 154.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
3850.2.c.r 3850.c 5.b $4$ $30.742$ \(\Q(\zeta_{12})\) None 3850.2.a.bk \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.s 3850.c 5.b $4$ $30.742$ \(\Q(\zeta_{12})\) None 770.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.t 3850.c 5.b $4$ $30.742$ \(\Q(i, \sqrt{10})\) None 3850.2.a.bf \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.u 3850.c 5.b $4$ $30.742$ \(\Q(\zeta_{8})\) None 770.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{2}+\beta_{2} q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
3850.2.c.v 3850.c 5.b $4$ $30.742$ \(\Q(i, \sqrt{7})\) None 3850.2.a.bh \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.w 3850.c 5.b $4$ $30.742$ \(\Q(\zeta_{8})\) None 3850.2.a.bg \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{2}+\beta_{2} q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
3850.2.c.x 3850.c 5.b $4$ $30.742$ \(\Q(\zeta_{12})\) None 770.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.y 3850.c 5.b $4$ $30.742$ \(\Q(i, \sqrt{33})\) None 770.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}+2q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.z 3850.c 5.b $6$ $30.742$ 6.0.3182656.1 None 770.2.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots\)
3850.2.c.ba 3850.c 5.b $6$ $30.742$ 6.0.399424.1 None 770.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.c.bb 3850.c 5.b $6$ $30.742$ 6.0.399424.1 None 3850.2.a.bs \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
3850.2.c.bc 3850.c 5.b $6$ $30.742$ 6.0.3534400.1 None 3850.2.a.br \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)