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

\( 68q - 4q^{3} - 4q^{7} + 60q^{9} + O(q^{10}) \) \( 68q - 4q^{3} - 4q^{7} + 60q^{9} + 4q^{11} + 4q^{17} - 16q^{19} - 4q^{21} - 4q^{23} - 16q^{27} + 4q^{33} + 24q^{47} + 20q^{51} + 4q^{53} + 12q^{57} + 32q^{59} - 36q^{61} - 12q^{63} + 20q^{69} + 72q^{71} + 8q^{73} + 32q^{77} + 28q^{81} + 36q^{83} + 52q^{87} + 36q^{91} + 4q^{97} + 76q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1600.2.s.a \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(-6\) \(q-2q^{3}+(-3-3i)q^{7}+q^{9}+(1-i)q^{11}+\cdots\)
1600.2.s.b \(8\) \(12.776\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+(-\zeta_{24}+\cdots)q^{7}+\cdots\)
1600.2.s.c \(16\) \(12.776\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{7}q^{7}+(1-\beta _{12})q^{9}+(-1+\cdots)q^{11}+\cdots\)
1600.2.s.d \(18\) \(12.776\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(1+\beta _{3})q^{9}+(-\beta _{13}+\cdots)q^{11}+\cdots\)
1600.2.s.e \(24\) \(12.776\) None \(0\) \(0\) \(0\) \(0\)

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

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