Properties

Label 3840.2.d
Level $3840$
Weight $2$
Character orbit 3840.d
Rep. character $\chi_{3840}(2689,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $38$
Sturm bound $1536$
Trace bound $35$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(1536\)
Trace bound: \(35\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(31\), \(37\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

Total New Old
Modular forms 816 96 720
Cusp forms 720 96 624
Eisenstein series 96 0 96

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \) \( 96 q + 96 q^{9} - 96 q^{49} + 32 q^{65} + 96 q^{81} + 64 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3840.2.d.a 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-2+i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.b 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-2-i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.c 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-2+i)q^{5}+q^{9}-2iq^{11}+\cdots\)
3840.2.d.d 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.e 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}-3iq^{11}+\cdots\)
3840.2.d.f 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1+i)q^{5}+q^{9}+2iq^{11}+\cdots\)
3840.2.d.g 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.h 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1+i)q^{5}+2iq^{7}+q^{9}+\cdots\)
3840.2.d.i 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(1+i)q^{5}+2iq^{7}+q^{9}-6q^{13}+\cdots\)
3840.2.d.j 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(1-i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.k 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(1+i)q^{5}+iq^{7}+q^{9}+3iq^{11}+\cdots\)
3840.2.d.l 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(1-i)q^{5}+q^{9}+2iq^{11}+2q^{13}+\cdots\)
3840.2.d.m 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(1+i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.n 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(2+i)q^{5}+q^{9}+2iq^{11}-2q^{13}+\cdots\)
3840.2.d.o 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(2-i)q^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots\)
3840.2.d.p 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(2+i)q^{5}+4iq^{7}+q^{9}+4q^{13}+\cdots\)
3840.2.d.q 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-2-i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.r 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-2+i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.s 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-2+i)q^{5}+q^{9}+2iq^{11}+\cdots\)
3840.2.d.t 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1+i)q^{5}+q^{9}-2iq^{11}+\cdots\)
3840.2.d.u 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}-3iq^{11}+\cdots\)
3840.2.d.v 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.w 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1-i)q^{5}+2iq^{7}+q^{9}+\cdots\)
3840.2.d.x 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.y 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(1+i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.z 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(1-i)q^{5}+2iq^{7}+q^{9}-6q^{13}+\cdots\)
3840.2.d.ba 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(1-i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.bb 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(1-i)q^{5}+q^{9}-2iq^{11}+2q^{13}+\cdots\)
3840.2.d.bc 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(1-i)q^{5}+iq^{7}+q^{9}+3iq^{11}+\cdots\)
3840.2.d.bd 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(2-i)q^{5}+q^{9}+2iq^{11}-2q^{13}+\cdots\)
3840.2.d.be 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(2+i)q^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots\)
3840.2.d.bf 3840.d 40.f $2$ $30.663$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(2-i)q^{5}+4iq^{7}+q^{9}+4q^{13}+\cdots\)
3840.2.d.bg 3840.d 40.f $4$ $30.663$ \(\Q(i, \sqrt{5})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
3840.2.d.bh 3840.d 40.f $4$ $30.663$ \(\Q(i, \sqrt{5})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
3840.2.d.bi 3840.d 40.f $6$ $30.663$ 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bj 3840.d 40.f $6$ $30.663$ 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bk 3840.d 40.f $6$ $30.663$ 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bl 3840.d 40.f $6$ $30.663$ 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)