Properties

Label 2304.3.e
Level $2304$
Weight $3$
Character orbit 2304.e
Rep. character $\chi_{2304}(1025,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $15$
Sturm bound $1152$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(1152\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2304, [\chi])\).

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

Trace form

\( 64q + O(q^{10}) \) \( 64q - 320q^{25} + 576q^{49} - 640q^{73} + 896q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2304.3.e.a \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+7\beta q^{5}-10q^{13}+23\beta q^{17}-73q^{25}+\cdots\)
2304.3.e.b \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-10q^{13}-7\beta q^{17}+23q^{25}+\cdots\)
2304.3.e.c \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+7\beta q^{5}+10q^{13}-23\beta q^{17}-73q^{25}+\cdots\)
2304.3.e.d \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+10q^{13}+7\beta q^{17}+23q^{25}+\cdots\)
2304.3.e.e \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}q^{11}-18q^{13}+\cdots\)
2304.3.e.f \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-10q^{13}+\cdots\)
2304.3.e.g \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{3}q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
2304.3.e.h \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+2\beta _{2}q^{11}+3\beta _{3}q^{13}+\cdots\)
2304.3.e.i \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{3}q^{7}-2\beta _{2}q^{11}+3\beta _{3}q^{13}+\cdots\)
2304.3.e.j \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{3}q^{7}+2\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots\)
2304.3.e.k \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{11}+10q^{13}+\cdots\)
2304.3.e.l \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}+18q^{13}+\cdots\)
2304.3.e.m \(8\) \(62.779\) 8.0.5473632256.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{5}+\beta _{5}q^{7}-\beta _{3}q^{11}-\beta _{4}q^{13}+\cdots\)
2304.3.e.n \(8\) \(62.779\) 8.0.\(\cdots\).16 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{3}q^{7}+(\beta _{2}+\beta _{4})q^{11}+\beta _{5}q^{13}+\cdots\)
2304.3.e.o \(8\) \(62.779\) 8.0.\(\cdots\).16 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{3}q^{7}+(-\beta _{2}-\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)