Properties

Label 1152.2.k
Level $1152$
Weight $2$
Character orbit 1152.k
Rep. character $\chi_{1152}(289,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $36$
Newform subspaces $6$
Sturm bound $384$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 448 44 404
Cusp forms 320 36 284
Eisenstein series 128 8 120

Trace form

\( 36q - 4q^{5} + O(q^{10}) \) \( 36q - 4q^{5} + 4q^{13} + 8q^{17} - 20q^{29} - 12q^{37} - 20q^{49} + 12q^{53} - 28q^{61} + 24q^{65} + 40q^{77} + 56q^{85} - 8q^{97} + O(q^{100}) \)

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.k.a \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+2iq^{7}+(-1-i)q^{11}+\cdots\)
1152.2.k.b \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-2iq^{7}+(1+i)q^{11}+\cdots\)
1152.2.k.c \(8\) \(9.199\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}-\beta _{6})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1152.2.k.d \(8\) \(9.199\) 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
1152.2.k.e \(8\) \(9.199\) 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
1152.2.k.f \(8\) \(9.199\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}-\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)