Properties

Label 4050.2.c
Level $4050$
Weight $2$
Character orbit 4050.c
Rep. character $\chi_{4050}(649,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $28$
Sturm bound $1620$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 4050 = 2 \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4050.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(1620\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(29\), \(41\), \(71\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4050, [\chi])\).

Total New Old
Modular forms 882 72 810
Cusp forms 738 72 666
Eisenstein series 144 0 144

Trace form

\( 72 q - 72 q^{4} + O(q^{10}) \) \( 72 q - 72 q^{4} + 72 q^{16} - 24 q^{31} - 12 q^{34} + 24 q^{46} - 144 q^{49} + 36 q^{61} - 72 q^{64} - 24 q^{79} + 24 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4050, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4050.2.c.a 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-6q^{11}+\cdots\)
4050.2.c.b 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-6q^{11}+\cdots\)
4050.2.c.c 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-3q^{11}+\cdots\)
4050.2.c.d 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-3q^{11}+\cdots\)
4050.2.c.e 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-3q^{11}+\cdots\)
4050.2.c.f 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+5iq^{7}-iq^{8}+iq^{13}+\cdots\)
4050.2.c.g 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-iq^{13}+\cdots\)
4050.2.c.h 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+4iq^{13}+\cdots\)
4050.2.c.i 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+5iq^{13}+\cdots\)
4050.2.c.j 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4iq^{13}+\cdots\)
4050.2.c.k 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+5iq^{13}+\cdots\)
4050.2.c.l 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-4iq^{13}+\cdots\)
4050.2.c.m 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+4iq^{13}+\cdots\)
4050.2.c.n 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-iq^{13}+\cdots\)
4050.2.c.o 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+5iq^{7}+iq^{8}+iq^{13}+\cdots\)
4050.2.c.p 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{11}+\cdots\)
4050.2.c.q 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{11}+\cdots\)
4050.2.c.r 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+3q^{11}+\cdots\)
4050.2.c.s 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+6q^{11}+\cdots\)
4050.2.c.t 4050.c 5.b $2$ $32.339$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+6q^{11}+\cdots\)
4050.2.c.u 4050.c 5.b $4$ $32.339$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.v 4050.c 5.b $4$ $32.339$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}-\beta _{2}q^{8}+(-2+\cdots)q^{11}+\cdots\)
4050.2.c.w 4050.c 5.b $4$ $32.339$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(2\beta _{1}-\beta _{2})q^{7}-\beta _{1}q^{8}+\cdots\)
4050.2.c.x 4050.c 5.b $4$ $32.339$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.y 4050.c 5.b $4$ $32.339$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(2\beta _{1}-\beta _{2})q^{7}+\beta _{1}q^{8}+\cdots\)
4050.2.c.z 4050.c 5.b $4$ $32.339$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.ba 4050.c 5.b $4$ $32.339$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+(2+\cdots)q^{11}+\cdots\)
4050.2.c.bb 4050.c 5.b $4$ $32.339$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-q^{4}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2025, [\chi])\)\(^{\oplus 2}\)