Properties

Label 2304.3.g
Level $2304$
Weight $3$
Character orbit 2304.g
Rep. character $\chi_{2304}(1279,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $26$
Sturm bound $1152$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(1152\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

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

\( 78q + O(q^{10}) \) \( 78q + 4q^{17} + 354q^{25} - 4q^{41} - 402q^{49} - 64q^{65} + 228q^{73} + 156q^{89} - 452q^{97} + O(q^{100}) \)

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.g.a \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-8\) \(0\) \(q-8q^{5}-24q^{13}-30q^{17}+39q^{25}+\cdots\)
2304.3.g.b \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}-24q^{13}+2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.c \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}+24q^{13}-2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.d \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+6q^{5}-24q^{13}-2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.e \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+6q^{5}+24q^{13}+2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.f \(1\) \(62.779\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(8\) \(0\) \(q+8q^{5}+24q^{13}-30q^{17}+39q^{25}+\cdots\)
2304.3.g.g \(2\) \(62.779\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-8\) \(0\) \(q-4q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+18q^{17}+\cdots\)
2304.3.g.h \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-8\) \(0\) \(q-4q^{5}-4\beta q^{7}+5\beta q^{11}+20q^{13}+\cdots\)
2304.3.g.i \(2\) \(62.779\) \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(-4\) \(0\) \(q-2q^{5}-\beta q^{7}+2\beta q^{11}-21q^{25}+\cdots\)
2304.3.g.j \(2\) \(62.779\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-7iq^{11}-2q^{17}+17iq^{19}-5^{2}q^{25}+\cdots\)
2304.3.g.k \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{11}+2q^{17}+\beta q^{19}-5^{2}q^{25}+\cdots\)
2304.3.g.l \(2\) \(62.779\) \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(4\) \(0\) \(q+2q^{5}-\beta q^{7}-2\beta q^{11}-21q^{25}+\cdots\)
2304.3.g.m \(2\) \(62.779\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(8\) \(0\) \(q+4q^{5}-4\beta q^{7}-5\beta q^{11}-20q^{13}+\cdots\)
2304.3.g.n \(2\) \(62.779\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(8\) \(0\) \(q+4q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{11}+18q^{17}+\cdots\)
2304.3.g.o \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-16\) \(0\) \(q+(-4+\beta _{2})q^{5}+\beta _{1}q^{7}+(4\beta _{1}-\beta _{3})q^{11}+\cdots\)
2304.3.g.p \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{11}-4q^{13}+\cdots\)
2304.3.g.q \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}-5\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2304.3.g.r \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.g.s \(4\) \(62.779\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
2304.3.g.t \(4\) \(62.779\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-5\beta _{1}q^{7}+\beta _{3}q^{11}+71q^{25}+\cdots\)
2304.3.g.u \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.g.v \(4\) \(62.779\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2304.3.g.w \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{11}+4q^{13}+\cdots\)
2304.3.g.x \(4\) \(62.779\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(16\) \(0\) \(q+(4+\beta _{2})q^{5}+\beta _{1}q^{7}+(-4\beta _{1}-\beta _{3})q^{11}+\cdots\)
2304.3.g.y \(8\) \(62.779\) 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{5}q^{7}+\beta _{4}q^{11}+\beta _{1}q^{13}+\cdots\)
2304.3.g.z \(8\) \(62.779\) 8.0.22581504.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{6}q^{11}+(\beta _{1}-\beta _{4}+\cdots)q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)