Properties

Label 2304.3.b
Level $2304$
Weight $3$
Character orbit 2304.b
Rep. character $\chi_{2304}(127,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $20$
Sturm bound $1152$
Trace bound $19$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(1152\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 816 82 734
Cusp forms 720 78 642
Eisenstein series 96 4 92

Trace form

\( 78q + O(q^{10}) \) \( 78q + 4q^{17} - 346q^{25} - 4q^{41} - 530q^{49} + 136q^{65} + 420q^{73} - 164q^{89} + 444q^{97} + O(q^{100}) \)

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.b.a \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{5}-2iq^{7}-2^{4}q^{11}-iq^{13}+\cdots\)
2304.3.b.b \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{5}-2iq^{7}-2^{4}q^{11}+iq^{13}+\cdots\)
2304.3.b.c \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-4iq^{7}-4q^{11}-7iq^{13}+\cdots\)
2304.3.b.d \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+4iq^{5}+5iq^{13}-2^{4}q^{17}-39q^{25}+\cdots\)
2304.3.b.e \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+4iq^{5}-5iq^{13}+2^{4}q^{17}-39q^{25}+\cdots\)
2304.3.b.f \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{5}-5iq^{13}+30q^{17}-11q^{25}+\cdots\)
2304.3.b.g \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+4iq^{7}+4q^{11}-7iq^{13}+\cdots\)
2304.3.b.h \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{5}+2iq^{7}+2^{4}q^{11}-iq^{13}+\cdots\)
2304.3.b.i \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{5}+2iq^{7}+2^{4}q^{11}+iq^{13}+\cdots\)
2304.3.b.j \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+(-2\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2304.3.b.k \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2304.3.b.l \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.b.m \(4\) \(62.779\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{7}-11\zeta_{12}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
2304.3.b.n \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}-3\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.b.o \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{5}+(2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
2304.3.b.p \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+(2\zeta_{8}-\zeta_{8}^{3})q^{7}+(10+\cdots)q^{11}+\cdots\)
2304.3.b.q \(8\) \(62.779\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{3})q^{5}+(\zeta_{24}+\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
2304.3.b.r \(8\) \(62.779\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(\beta _{1}+\beta _{6})q^{7}-\beta _{4}q^{11}+(3\beta _{1}+\cdots)q^{13}+\cdots\)
2304.3.b.s \(8\) \(62.779\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+\beta _{4}q^{11}+\cdots\)
2304.3.b.t \(8\) \(62.779\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{3})q^{5}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)