Properties

Label 1216.2.h
Level $1216$
Weight $2$
Character orbit 1216.h
Rep. character $\chi_{1216}(1215,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $5$
Sturm bound $320$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(320\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 172 42 130
Cusp forms 148 38 110
Eisenstein series 24 4 20

Trace form

\( 38q + 4q^{5} + 30q^{9} + O(q^{10}) \) \( 38q + 4q^{5} + 30q^{9} - 4q^{17} + 26q^{25} + 36q^{45} - 30q^{49} - 16q^{57} - 12q^{61} - 4q^{73} + 22q^{81} + 16q^{85} + 32q^{93} + O(q^{100}) \)

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.h.a \(2\) \(9.710\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
1216.2.h.b \(4\) \(9.710\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
1216.2.h.c \(4\) \(9.710\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
1216.2.h.d \(8\) \(9.710\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}-\beta _{7}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1216.2.h.e \(20\) \(9.710\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{14}q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)