Properties

Label 1600.2.s
Level $1600$
Weight $2$
Character orbit 1600.s
Rep. character $\chi_{1600}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $5$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

Total New Old
Modular forms 528 76 452
Cusp forms 432 68 364
Eisenstein series 96 8 88

Trace form

\( 68 q - 4 q^{3} - 4 q^{7} + 60 q^{9} + 4 q^{11} + 4 q^{17} - 16 q^{19} - 4 q^{21} - 4 q^{23} - 16 q^{27} + 4 q^{33} + 24 q^{47} + 20 q^{51} + 4 q^{53} + 12 q^{57} + 32 q^{59} - 36 q^{61} - 12 q^{63} + 20 q^{69}+ \cdots + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.2.s.a 1600.s 80.s $2$ $12.776$ \(\Q(\sqrt{-1}) \) None 80.2.j.a \(0\) \(-4\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q-2 q^{3}+(-3 i-3)q^{7}+q^{9}+(-i+1)q^{11}+\cdots\)
1600.2.s.b 1600.s 80.s $8$ $12.776$ \(\Q(\zeta_{24})\) None 400.2.j.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_{7}+\beta_{5}+\beta_1)q^{3}+(-\beta_{7}+2\beta_{5}+\cdots-\beta_1)q^{7}+\cdots\)
1600.2.s.c 1600.s 80.s $16$ $12.776$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 400.2.j.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}-\beta _{7}q^{7}+(1-\beta _{12})q^{9}+(-1+\cdots)q^{11}+\cdots\)
1600.2.s.d 1600.s 80.s $18$ $12.776$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 80.2.j.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(1+\beta _{3})q^{9}+(-\beta _{13}+\cdots)q^{11}+\cdots\)
1600.2.s.e 1600.s 80.s $24$ $12.776$ None 400.2.j.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)