Properties

Label 1152.2.c
Level $1152$
Weight $2$
Character orbit 1152.c
Rep. character $\chi_{1152}(1151,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $384$
Trace bound $35$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(35\)
Distinguishing \(T_p\): \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

Total New Old
Modular forms 224 16 208
Cusp forms 160 16 144
Eisenstein series 64 0 64

Trace form

\( 16q + O(q^{10}) \) \( 16q - 16q^{25} - 80q^{49} + 64q^{73} + 128q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1152.2.c.a \(4\) \(9.199\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
1152.2.c.b \(4\) \(9.199\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\)
1152.2.c.c \(4\) \(9.199\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
1152.2.c.d \(4\) \(9.199\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)