Properties

Label 800.2.c
Level $800$
Weight $2$
Character orbit 800.c
Rep. character $\chi_{800}(449,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $7$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 144 18 126
Cusp forms 96 18 78
Eisenstein series 48 0 48

Trace form

\( 18q - 18q^{9} + O(q^{10}) \) \( 18q - 18q^{9} + 16q^{21} - 12q^{29} + 28q^{41} - 18q^{49} - 20q^{61} - 64q^{69} - 62q^{81} + 20q^{89} + O(q^{100}) \)

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.c.a \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots\)
800.2.c.b \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots\)
800.2.c.c \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{7}+2q^{9}-5q^{11}+5iq^{17}+\cdots\)
800.2.c.d \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{7}+2q^{9}+5q^{11}-5iq^{17}+\cdots\)
800.2.c.e \(2\) \(6.388\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3q^{9}+3iq^{13}-iq^{17}+10q^{29}+\cdots\)
800.2.c.f \(4\) \(6.388\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{7}-5q^{9}+\zeta_{8}^{3}q^{11}+\cdots\)
800.2.c.g \(4\) \(6.388\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-2\beta _{2}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)