Properties

Label 1216.2.c
Level $1216$
Weight $2$
Character orbit 1216.c
Rep. character $\chi_{1216}(609,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $9$
Sturm bound $320$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(320\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

Total New Old
Modular forms 172 36 136
Cusp forms 148 36 112
Eisenstein series 24 0 24

Trace form

\( 36q - 36q^{9} + O(q^{10}) \) \( 36q - 36q^{9} + 24q^{17} - 60q^{25} - 24q^{41} + 36q^{49} + 24q^{73} + 132q^{81} - 72q^{89} - 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1216.2.c.a \(2\) \(9.710\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-6\) \(q+iq^{3}-3q^{7}+2q^{9}-3iq^{13}+3q^{17}+\cdots\)
1216.2.c.b \(2\) \(9.710\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+3iq^{3}-4iq^{5}-q^{7}-6q^{9}+5iq^{13}+\cdots\)
1216.2.c.c \(2\) \(9.710\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+3iq^{3}+4iq^{5}+q^{7}-6q^{9}-5iq^{13}+\cdots\)
1216.2.c.d \(2\) \(9.710\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(6\) \(q+iq^{3}+3q^{7}+2q^{9}+3iq^{13}+3q^{17}+\cdots\)
1216.2.c.e \(4\) \(9.710\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.f \(4\) \(9.710\) \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}-5\beta _{1}q^{11}+\cdots\)
1216.2.c.g \(4\) \(9.710\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1216.2.c.h \(8\) \(9.710\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{3}+2\beta _{6})q^{7}+\cdots\)
1216.2.c.i \(8\) \(9.710\) 8.0.2702336256.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{5}q^{7}+3q^{9}+(-\beta _{2}-2\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)