Properties

Label 1920.2.d
Level $1920$
Weight $2$
Character orbit 1920.d
Rep. character $\chi_{1920}(1729,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $8$
Sturm bound $768$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1920.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(768\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(13\), \(31\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1920, [\chi])\).

Total New Old
Modular forms 416 48 368
Cusp forms 352 48 304
Eisenstein series 64 0 64

Trace form

\( 48 q + 48 q^{9} + 16 q^{25} - 32 q^{41} - 48 q^{49} + 32 q^{65} + 48 q^{81} + 96 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1920, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1920.2.d.a 1920.d 40.f $4$ $15.331$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 1920.2.d.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{1}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{13}+\cdots\)
1920.2.d.b 1920.d 40.f $4$ $15.331$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 1920.2.d.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{13}+\cdots\)
1920.2.d.c 1920.d 40.f $6$ $15.331$ 6.0.350464.1 None 1920.2.d.c \(0\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
1920.2.d.d 1920.d 40.f $6$ $15.331$ 6.0.350464.1 None 1920.2.d.c \(0\) \(-6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{4}q^{5}-\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
1920.2.d.e 1920.d 40.f $6$ $15.331$ 6.0.350464.1 None 1920.2.d.c \(0\) \(6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{4}q^{5}-\beta _{5}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
1920.2.d.f 1920.d 40.f $6$ $15.331$ 6.0.350464.1 None 1920.2.d.c \(0\) \(6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{3}q^{5}-\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
1920.2.d.g 1920.d 40.f $8$ $15.331$ 8.0.3288334336.1 None 1920.2.d.g \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{7}q^{11}+\cdots\)
1920.2.d.h 1920.d 40.f $8$ $15.331$ 8.0.3288334336.1 None 1920.2.d.g \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)