Properties

Label 1650.2.c
Level $1650$
Weight $2$
Character orbit 1650.c
Rep. character $\chi_{1650}(199,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $15$
Sturm bound $720$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1650.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(720\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).

Total New Old
Modular forms 384 32 352
Cusp forms 336 32 304
Eisenstein series 48 0 48

Trace form

\( 32 q - 32 q^{4} - 32 q^{9} + O(q^{10}) \) \( 32 q - 32 q^{4} - 32 q^{9} + 32 q^{16} - 8 q^{19} + 8 q^{21} + 24 q^{26} - 24 q^{29} - 24 q^{31} - 40 q^{34} + 32 q^{36} - 8 q^{39} - 8 q^{41} - 24 q^{49} + 32 q^{59} - 32 q^{64} + 8 q^{66} - 16 q^{69} - 96 q^{71} - 24 q^{74} + 8 q^{76} - 8 q^{79} + 32 q^{81} - 8 q^{84} - 32 q^{86} + 24 q^{89} + 32 q^{91} - 32 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1650.2.c.a 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.b 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
1650.2.c.c 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.d 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.e 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.f 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
1650.2.c.g 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.h 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.i 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
1650.2.c.j 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1650.2.c.k 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
1650.2.c.l 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.m 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.n 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.o 1650.c 5.b $4$ $13.175$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)