Properties

Label 3520.2.f
Level $3520$
Weight $2$
Character orbit 3520.f
Rep. character $\chi_{3520}(2111,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $13$
Sturm bound $1152$
Trace bound $33$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1152\)
Trace bound: \(33\)
Distinguishing \(T_p\): \(3\), \(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

Total New Old
Modular forms 600 96 504
Cusp forms 552 96 456
Eisenstein series 48 0 48

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \) \( 96 q - 96 q^{9} + 96 q^{25} + 16 q^{33} + 32 q^{37} + 96 q^{49} + 32 q^{53} - 16 q^{77} + 64 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3520.2.f.a 3520.f 44.c $2$ $28.107$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{5}-4q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
3520.2.f.b 3520.f 44.c $2$ $28.107$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots\)
3520.2.f.c 3520.f 44.c $2$ $28.107$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{5}+q^{9}+(3-\beta )q^{11}+3\beta q^{13}+\cdots\)
3520.2.f.d 3520.f 44.c $2$ $28.107$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{5}+4q^{7}+q^{9}+(-3+\beta )q^{11}+\cdots\)
3520.2.f.e 3520.f 44.c $4$ $28.107$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{5}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
3520.2.f.f 3520.f 44.c $4$ $28.107$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{5}-q^{9}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
3520.2.f.g 3520.f 44.c $4$ $28.107$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-q^{5}-2\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
3520.2.f.h 3520.f 44.c $8$ $28.107$ 8.0.170772624.1 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-q^{5}+\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
3520.2.f.i 3520.f 44.c $8$ $28.107$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+q^{5}-\beta _{3}q^{7}+(-3+\beta _{7})q^{9}+\cdots\)
3520.2.f.j 3520.f 44.c $8$ $28.107$ 8.0.170772624.1 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+q^{5}-\beta _{1}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
3520.2.f.k 3520.f 44.c $12$ $28.107$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-q^{5}-\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.f.l 3520.f 44.c $16$ $28.107$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}-q^{5}-\beta _{9}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.f.m 3520.f 44.c $24$ $28.107$ None \(0\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)