Properties

Label 2736.1.o
Level $2736$
Weight $1$
Character orbit 2736.o
Rep. character $\chi_{2736}(721,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $480$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2736.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(480\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2736, [\chi])\).

Total New Old
Modular forms 54 5 49
Cusp forms 30 4 26
Eisenstein series 24 1 23

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + q^{5} + q^{7} + O(q^{10}) \) \( 4q + q^{5} + q^{7} - q^{11} + q^{17} + 2q^{19} + 2q^{23} + 3q^{25} + q^{35} + q^{43} - q^{47} + 3q^{49} + 5q^{55} - q^{61} - q^{73} - q^{77} + 2q^{83} - 5q^{85} - q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2736.1.o.a \(1\) \(1.365\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(2\) \(q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots\)
2736.1.o.b \(1\) \(1.365\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots\)
2736.1.o.c \(2\) \(1.365\) \(\Q(\sqrt{3}) \) \(D_{6}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)