Properties

Label 1600.2.l
Level $1600$
Weight $2$
Character orbit 1600.l
Rep. character $\chi_{1600}(401,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $70$
Newform subspaces $9$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 9 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 528 82 446
Cusp forms 432 70 362
Eisenstein series 96 12 84

Trace form

\( 70q - 2q^{3} + O(q^{10}) \) \( 70q - 2q^{3} + 2q^{11} + 2q^{13} + 4q^{17} + 6q^{19} - 12q^{21} + 16q^{27} + 10q^{29} + 4q^{33} + 10q^{37} + 18q^{43} - 24q^{47} - 30q^{49} - 28q^{51} - 6q^{53} - 30q^{59} + 10q^{61} + 44q^{63} + 30q^{67} + 36q^{69} - 20q^{77} - 34q^{81} + 38q^{83} + 60q^{91} + 32q^{93} + 4q^{97} - 18q^{99} + O(q^{100}) \)

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.l.a \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+i)q^{3}-2iq^{7}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
1600.2.l.b \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+i)q^{3}+iq^{9}+(3+3i)q^{11}+\cdots\)
1600.2.l.c \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1-i)q^{3}+iq^{9}+(3+3i)q^{11}+(-3+\cdots)q^{13}+\cdots\)
1600.2.l.d \(4\) \(12.776\) \(\Q(i, \sqrt{11})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
1600.2.l.e \(4\) \(12.776\) \(\Q(i, \sqrt{11})\) None \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
1600.2.l.f \(12\) \(12.776\) 12.0.\(\cdots\).1 None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(\beta _{2}+\beta _{3})q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1600.2.l.g \(12\) \(12.776\) 12.0.\(\cdots\).1 None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{4}q^{3}+(-\beta _{2}-\beta _{3})q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1600.2.l.h \(16\) \(12.776\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots\)
1600.2.l.i \(16\) \(12.776\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+(-\beta _{3}-\beta _{6}-\beta _{8}+\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)