Properties

Label 2352.2.q
Level $2352$
Weight $2$
Character orbit 2352.q
Rep. character $\chi_{2352}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $33$
Sturm bound $896$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 33 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 992 80 912
Cusp forms 800 80 720
Eisenstein series 192 0 192

Trace form

\( 80q + 2q^{3} - 40q^{9} + O(q^{10}) \) \( 80q + 2q^{3} - 40q^{9} - 8q^{11} + 10q^{19} - 20q^{23} - 36q^{25} - 4q^{27} - 32q^{29} - 14q^{31} + 4q^{33} + 16q^{37} - 2q^{39} - 16q^{41} + 20q^{43} + 12q^{47} + 24q^{53} + 56q^{55} + 8q^{57} + 16q^{59} + 8q^{61} + 8q^{65} + 2q^{67} - 16q^{71} - 12q^{73} + 14q^{75} - 22q^{79} - 40q^{81} + 24q^{83} + 32q^{85} - 12q^{87} - 16q^{89} - 16q^{93} + 60q^{95} - 8q^{97} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.2.q.a \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.b \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.c \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.d \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.e \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.f \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.2.q.g \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.h \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4+\cdots)q^{17}+\cdots\)
2352.2.q.i \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.j \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.k \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.l \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.m \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.n \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.o \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-2q^{13}+\cdots\)
2352.2.q.p \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.q \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.r \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.s \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.t \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
2352.2.q.u \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(5-5\zeta_{6})q^{11}+\cdots\)
2352.2.q.v \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2352.2.q.w \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}-6q^{13}+\cdots\)
2352.2.q.x \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.y \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.z \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.ba \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bb \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bc \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bd \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.be \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bf \(4\) \(18.781\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(2\) \(-1\) \(0\) \(q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.q.bg \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)