Properties

Label 4650.2.d
Level $4650$
Weight $2$
Character orbit 4650.d
Rep. character $\chi_{4650}(3349,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $36$
Sturm bound $1920$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(1920\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4650, [\chi])\).

Total New Old
Modular forms 984 92 892
Cusp forms 936 92 844
Eisenstein series 48 0 48

Trace form

\( 92q - 92q^{4} - 92q^{9} + O(q^{10}) \) \( 92q - 92q^{4} - 92q^{9} + 16q^{14} + 92q^{16} - 8q^{19} + 8q^{26} - 24q^{29} - 24q^{34} + 92q^{36} + 8q^{41} - 16q^{46} - 76q^{49} - 24q^{51} - 16q^{56} + 8q^{61} - 92q^{64} + 16q^{66} - 64q^{71} - 8q^{74} + 8q^{76} + 96q^{79} + 92q^{81} - 32q^{86} + 88q^{89} - 96q^{91} - 48q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4650, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4650.2.d.a \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
4650.2.d.b \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.c \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
4650.2.d.d \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.e \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.f \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
4650.2.d.g \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.h \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
4650.2.d.i \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.j \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
4650.2.d.k \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.l \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
4650.2.d.m \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
4650.2.d.n \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
4650.2.d.o \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
4650.2.d.p \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.q \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.r \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.s \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots\)
4650.2.d.t \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.u \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.v \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
4650.2.d.w \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.x \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.y \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.z \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.ba \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.bb \(2\) \(37.130\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.bc \(4\) \(37.130\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+2\beta _{1}q^{7}+\cdots\)
4650.2.d.bd \(4\) \(37.130\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.be \(4\) \(37.130\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4650.2.d.bf \(4\) \(37.130\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}-3\beta _{1}q^{7}+\cdots\)
4650.2.d.bg \(4\) \(37.130\) \(\Q(i, \sqrt{65})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.bh \(4\) \(37.130\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.bi \(6\) \(37.130\) 6.0.44836416.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-q^{6}-\beta _{4}q^{7}+\cdots\)
4650.2.d.bj \(6\) \(37.130\) 6.0.120648256.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+(\beta _{2}+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2325, [\chi])\)\(^{\oplus 2}\)