Properties

Label 800.2.o
Level $800$
Weight $2$
Character orbit 800.o
Rep. character $\chi_{800}(143,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $8$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

Total New Old
Modular forms 288 40 248
Cusp forms 192 32 160
Eisenstein series 96 8 88

Trace form

\( 32q - 4q^{3} + O(q^{10}) \) \( 32q - 4q^{3} + 8q^{11} + 8q^{17} + 8q^{27} + 16q^{33} - 8q^{41} + 28q^{43} + 40q^{51} - 8q^{57} - 28q^{67} - 16q^{73} - 40q^{81} - 44q^{83} - 56q^{91} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
800.2.o.a \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-4\) \(0\) \(0\) \(q+(-2+2i)q^{3}-5iq^{9}+6q^{11}+(4+\cdots)q^{17}+\cdots\)
800.2.o.b \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(-4\) \(q+(-2+2i)q^{7}+3iq^{9}-2q^{11}+(-4+\cdots)q^{13}+\cdots\)
800.2.o.c \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(4\) \(q+(2-2i)q^{7}+3iq^{9}-2q^{11}+(4+4i)q^{13}+\cdots\)
800.2.o.d \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(4\) \(0\) \(0\) \(q+(2-2i)q^{3}-5iq^{9}+6q^{11}+(-4+\cdots)q^{17}+\cdots\)
800.2.o.e \(4\) \(6.388\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+2\beta _{2}+\cdots)q^{9}+\cdots\)
800.2.o.f \(4\) \(6.388\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+2\beta _{2}+2\beta _{3})q^{9}+\cdots\)
800.2.o.g \(8\) \(6.388\) \(\Q(\zeta_{20})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\zeta_{20}^{2})q^{3}-\zeta_{20}^{7}q^{7}+(1+\zeta_{20}+\cdots)q^{9}+\cdots\)
800.2.o.h \(8\) \(6.388\) 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{6}q^{7}+q^{11}-\beta _{4}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)