Properties

Label 3200.2.d
Level $3200$
Weight $2$
Character orbit 3200.d
Rep. character $\chi_{3200}(1601,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $23$
Sturm bound $960$
Trace bound $33$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(960\)
Trace bound: \(33\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3200, [\chi])\).

Total New Old
Modular forms 528 76 452
Cusp forms 432 76 356
Eisenstein series 96 0 96

Trace form

\( 76q - 76q^{9} + O(q^{10}) \) \( 76q - 76q^{9} - 8q^{17} - 16q^{33} + 24q^{41} + 44q^{49} + 48q^{57} + 56q^{73} + 28q^{81} + 56q^{89} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3200.2.d.a \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\)
3200.2.d.b \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\)
3200.2.d.c \(2\) \(25.552\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-5q^{9}-\beta q^{11}-6q^{17}+3\beta q^{19}+\cdots\)
3200.2.d.d \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3q^{9}-3iq^{13}-8q^{17}-2iq^{29}+\cdots\)
3200.2.d.e \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3q^{9}-iq^{13}+2q^{17}+iq^{29}-3iq^{37}+\cdots\)
3200.2.d.f \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3q^{9}+3iq^{13}+8q^{17}-2iq^{29}+\cdots\)
3200.2.d.g \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\)
3200.2.d.h \(2\) \(25.552\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\)
3200.2.d.i \(4\) \(25.552\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-3\beta _{1}q^{7}-7q^{9}+3\beta _{3}q^{21}+\cdots\)
3200.2.d.j \(4\) \(25.552\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{3}q^{7}-7q^{9}+3\beta _{1}q^{13}+\cdots\)
3200.2.d.k \(4\) \(25.552\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots\)
3200.2.d.l \(4\) \(25.552\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{3}q^{7}-3q^{9}+2\beta _{2}q^{11}+\cdots\)
3200.2.d.m \(4\) \(25.552\) \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{1}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots\)
3200.2.d.n \(4\) \(25.552\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
3200.2.d.o \(4\) \(25.552\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
3200.2.d.p \(4\) \(25.552\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
3200.2.d.q \(4\) \(25.552\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
3200.2.d.r \(4\) \(25.552\) \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{1}q^{7}-2q^{9}-\beta _{3}q^{11}+\cdots\)
3200.2.d.s \(4\) \(25.552\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+3\zeta_{8}^{3}q^{7}+q^{9}+4\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.t \(4\) \(25.552\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}-2\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.u \(4\) \(25.552\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{21}-3\beta _{2}q^{23}+\cdots\)
3200.2.d.v \(4\) \(25.552\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}+2\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.w \(4\) \(25.552\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\beta _{3}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)