Properties

Label 1600.2.q
Level $1600$
Weight $2$
Character orbit 1600.q
Rep. character $\chi_{1600}(49,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $8$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(7\)
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

\( 68q + O(q^{10}) \) \( 68q + 4q^{11} - 20q^{19} + 8q^{21} + 4q^{29} + 32q^{31} + 52q^{49} + 28q^{59} + 28q^{61} - 40q^{69} + 64q^{79} - 44q^{81} + 8q^{91} + 84q^{99} + O(q^{100}) \)

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.q.a \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(-4\) \(q+(-1-i)q^{3}-2q^{7}-iq^{9}+(-1+\cdots)q^{11}+\cdots\)
1600.2.q.b \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(4\) \(q+(1+i)q^{3}+2q^{7}-iq^{9}+(-1-i)q^{11}+\cdots\)
1600.2.q.c \(4\) \(12.776\) \(\Q(i, \sqrt{11})\) None \(0\) \(-2\) \(0\) \(4\) \(q+(-1+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1600.2.q.d \(4\) \(12.776\) \(\Q(i, \sqrt{11})\) None \(0\) \(2\) \(0\) \(-4\) \(q+(\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)
1600.2.q.e \(12\) \(12.776\) 12.0.\(\cdots\).1 None \(0\) \(-2\) \(0\) \(12\) \(q+\beta _{4}q^{3}+(1+\beta _{5})q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1600.2.q.f \(12\) \(12.776\) 12.0.\(\cdots\).1 None \(0\) \(2\) \(0\) \(-12\) \(q-\beta _{4}q^{3}+(-1-\beta _{5})q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1600.2.q.g \(16\) \(12.776\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{6}q^{3}+(-\beta _{6}+\beta _{9}+\beta _{10}+\beta _{15})q^{7}+\cdots\)
1600.2.q.h \(16\) \(12.776\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{6}q^{3}+(\beta _{6}-\beta _{9}-\beta _{10}-\beta _{15})q^{7}+\cdots\)

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

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