Properties

Label 816.2.c
Level $816$
Weight $2$
Character orbit 816.c
Rep. character $\chi_{816}(577,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $6$
Sturm bound $288$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 816.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).

Total New Old
Modular forms 156 18 138
Cusp forms 132 18 114
Eisenstein series 24 0 24

Trace form

\( 18q - 18q^{9} + O(q^{10}) \) \( 18q - 18q^{9} + 4q^{13} + 4q^{15} + 2q^{17} - 20q^{19} - 14q^{25} - 24q^{35} - 12q^{43} - 24q^{47} - 18q^{49} + 4q^{51} + 12q^{53} + 20q^{55} + 56q^{59} + 24q^{67} + 16q^{69} - 16q^{77} + 18q^{81} - 16q^{85} - 20q^{89} - 16q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(816, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
816.2.c.a \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots\)
816.2.c.b \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots\)
816.2.c.c \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots\)
816.2.c.d \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots\)
816.2.c.e \(4\) \(6.516\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots\)
816.2.c.f \(6\) \(6.516\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(816, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(816, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)