Properties

Label 1600.2.n
Level $1600$
Weight $2$
Character orbit 1600.n
Rep. character $\chi_{1600}(1343,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $22$
Sturm bound $480$
Trace bound $21$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 22 \)
Sturm bound: \(480\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 552 76 476
Cusp forms 408 68 340
Eisenstein series 144 8 136

Trace form

\( 68q + O(q^{10}) \) \( 68q - 4q^{13} + 12q^{17} + 8q^{21} - 8q^{33} - 4q^{37} - 8q^{41} - 52q^{53} + 16q^{57} + 72q^{61} + 12q^{73} + 72q^{77} - 108q^{81} + 56q^{93} + 28q^{97} + O(q^{100}) \)

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.n.a \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(4\) \(q+(-2-2i)q^{3}+(2-2i)q^{7}+5iq^{9}+\cdots\)
1600.2.n.b \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(-2\) \(0\) \(-6\) \(q+(-1-i)q^{3}+(-3+3i)q^{7}-iq^{9}+\cdots\)
1600.2.n.c \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(-6\) \(q+(-1-i)q^{3}+(-3+3i)q^{7}-iq^{9}+\cdots\)
1600.2.n.d \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1-i)q^{3}+(1-i)q^{7}-iq^{9}+4iq^{11}+\cdots\)
1600.2.n.e \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1-i)q^{3}+(1-i)q^{7}-iq^{9}+6iq^{11}+\cdots\)
1600.2.n.f \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1-i)q^{3}+(1-i)q^{7}-iq^{9}-4iq^{11}+\cdots\)
1600.2.n.g \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{9}+(-5+5i)q^{13}+(5+5i)q^{17}+\cdots\)
1600.2.n.h \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{9}+(-1+i)q^{13}+(-3-3i)q^{17}+\cdots\)
1600.2.n.i \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(1+i)q^{3}+(-1+i)q^{7}-iq^{9}-4iq^{11}+\cdots\)
1600.2.n.j \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(1+i)q^{3}+(-1+i)q^{7}-iq^{9}-6iq^{11}+\cdots\)
1600.2.n.k \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(1+i)q^{3}+(-1+i)q^{7}-iq^{9}+4iq^{11}+\cdots\)
1600.2.n.l \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(2\) \(0\) \(6\) \(q+(1+i)q^{3}+(3-3i)q^{7}-iq^{9}+6q^{21}+\cdots\)
1600.2.n.m \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(6\) \(q+(1+i)q^{3}+(3-3i)q^{7}-iq^{9}+2iq^{11}+\cdots\)
1600.2.n.n \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(-4\) \(q+(2+2i)q^{3}+(-2+2i)q^{7}+5iq^{9}+\cdots\)
1600.2.n.o \(4\) \(12.776\) \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+2\beta _{2}+\cdots)q^{7}+\cdots\)
1600.2.n.p \(4\) \(12.776\) \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+2\beta _{2}+\cdots)q^{7}+\cdots\)
1600.2.n.q \(4\) \(12.776\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{7}-7\beta _{1}q^{9}-10q^{21}+\cdots\)
1600.2.n.r \(4\) \(12.776\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{7}+3\zeta_{12}q^{9}+\cdots\)
1600.2.n.s \(4\) \(12.776\) \(\Q(i, \sqrt{6})\) None \(0\) \(4\) \(0\) \(8\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(2-2\beta _{2})q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
1600.2.n.t \(4\) \(12.776\) \(\Q(i, \sqrt{6})\) None \(0\) \(4\) \(0\) \(8\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(2-2\beta _{2})q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
1600.2.n.u \(8\) \(12.776\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{3}-4\zeta_{24}q^{7}+2\zeta_{24}^{3}q^{9}+\cdots\)
1600.2.n.v \(8\) \(12.776\) 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+2\beta _{3}q^{9}+\beta _{7}q^{11}+2\beta _{4}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)