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

\( 92 q - 92 q^{4} - 108 q^{9} + O(q^{10}) \) \( 92 q - 92 q^{4} - 108 q^{9} + 4 q^{11} - 8 q^{14} + 92 q^{16} + 24 q^{26} - 40 q^{29} + 24 q^{31} - 40 q^{34} + 108 q^{36} + 48 q^{39} - 40 q^{41} - 4 q^{44} - 92 q^{49} + 16 q^{51} + 8 q^{56} + 88 q^{59} + 8 q^{61} - 92 q^{64} + 16 q^{69} - 8 q^{71} - 8 q^{74} - 32 q^{79} + 140 q^{81} + 24 q^{86} - 80 q^{89} + 8 q^{91} - 52 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3850.2.c.a \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.b \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.c \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
3850.2.c.d \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.e \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.f \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
3850.2.c.g \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
3850.2.c.h \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.i \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.j \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.k \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.l \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.m \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.n \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
3850.2.c.o \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots\)
3850.2.c.p \(2\) \(30.742\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
3850.2.c.q \(4\) \(30.742\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
3850.2.c.r \(4\) \(30.742\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.s \(4\) \(30.742\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.t \(4\) \(30.742\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.u \(4\) \(30.742\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
3850.2.c.v \(4\) \(30.742\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.w \(4\) \(30.742\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
3850.2.c.x \(4\) \(30.742\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.y \(4\) \(30.742\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}+2q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.z \(6\) \(30.742\) 6.0.3182656.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots\)
3850.2.c.ba \(6\) \(30.742\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.c.bb \(6\) \(30.742\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
3850.2.c.bc \(6\) \(30.742\) 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

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

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