Properties

Label 3120.2.l
Level $3120$
Weight $2$
Character orbit 3120.l
Rep. character $\chi_{3120}(1249,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $17$
Sturm bound $1344$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(1344\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

Total New Old
Modular forms 696 72 624
Cusp forms 648 72 576
Eisenstein series 48 0 48

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \) \( 72 q - 72 q^{9} - 32 q^{19} - 8 q^{25} - 16 q^{31} + 48 q^{35} + 8 q^{39} - 56 q^{49} + 8 q^{51} + 16 q^{55} - 16 q^{61} + 16 q^{69} - 8 q^{75} - 8 q^{79} + 72 q^{81} - 16 q^{85} + 24 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3120.2.l.a 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(-2-i)q^{5}-q^{9}+6q^{11}+\cdots\)
3120.2.l.b 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-2i)q^{5}+5iq^{7}-q^{9}+\cdots\)
3120.2.l.c 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-2i)q^{5}+iq^{7}-q^{9}+\cdots\)
3120.2.l.d 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+2i)q^{5}+iq^{7}-q^{9}+\cdots\)
3120.2.l.e 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(1-2i)q^{5}+iq^{7}-q^{9}-3q^{11}+\cdots\)
3120.2.l.f 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-2i)q^{5}+3iq^{7}-q^{9}+\cdots\)
3120.2.l.g 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots\)
3120.2.l.h 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2+i)q^{5}+4iq^{7}-q^{9}-2q^{11}+\cdots\)
3120.2.l.i 3120.l 5.b $2$ $24.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2-i)q^{5}+4iq^{7}-q^{9}+6q^{11}+\cdots\)
3120.2.l.j 3120.l 5.b $4$ $24.913$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-2\beta _{2}q^{7}+\cdots\)
3120.2.l.k 3120.l 5.b $4$ $24.913$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3120.2.l.l 3120.l 5.b $4$ $24.913$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots\)
3120.2.l.m 3120.l 5.b $6$ $24.913$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(2-\beta _{4}-\beta _{5})q^{11}+\cdots\)
3120.2.l.n 3120.l 5.b $8$ $24.913$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{6}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
3120.2.l.o 3120.l 5.b $8$ $24.913$ 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+\beta _{4}q^{7}+\cdots\)
3120.2.l.p 3120.l 5.b $10$ $24.913$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{9})q^{7}+\cdots\)
3120.2.l.q 3120.l 5.b $10$ $24.913$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+\beta _{3}q^{5}-\beta _{9}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)