Properties

Label 800.2.f
Level $800$
Weight $2$
Character orbit 800.f
Rep. character $\chi_{800}(49,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $5$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 144 20 124
Cusp forms 96 16 80
Eisenstein series 48 4 44

Trace form

\( 16q + 16q^{9} + O(q^{10}) \) \( 16q + 16q^{9} + 32q^{31} + 24q^{39} - 8q^{41} - 56q^{71} - 8q^{79} - 8q^{81} - 32q^{89} + O(q^{100}) \)

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.f.a \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-2iq^{7}-2q^{9}+5iq^{11}+6q^{13}+\cdots\)
800.2.f.b \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+2iq^{7}-2q^{9}+5iq^{11}-6q^{13}+\cdots\)
800.2.f.c \(4\) \(6.388\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{12})q^{3}+\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\)
800.2.f.d \(4\) \(6.388\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+4\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots\)
800.2.f.e \(4\) \(6.388\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{12})q^{3}-\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\)

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

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