Properties

Label 3240.2.q
Level $3240$
Weight $2$
Character orbit 3240.q
Rep. character $\chi_{3240}(1081,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $34$
Sturm bound $1296$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 34 \)
Sturm bound: \(1296\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).

Total New Old
Modular forms 1392 96 1296
Cusp forms 1200 96 1104
Eisenstein series 192 0 192

Trace form

\( 96q + O(q^{10}) \) \( 96q + 24q^{19} - 48q^{25} - 60q^{31} - 72q^{43} - 60q^{49} - 12q^{61} - 12q^{67} - 72q^{73} + 120q^{91} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3240.2.q.a \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.b \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
3240.2.q.c \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
3240.2.q.d \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.e \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+3q^{17}+\cdots\)
3240.2.q.f \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{11}-7q^{19}+6\zeta_{6}q^{23}+\cdots\)
3240.2.q.g \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-6\zeta_{6}q^{13}+\cdots\)
3240.2.q.h \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.i \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(2\) \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.j \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(2\) \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
3240.2.q.k \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
3240.2.q.l \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.m \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-4\) \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.n \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.o \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
3240.2.q.p \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
3240.2.q.q \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}-6\zeta_{6}q^{13}+\cdots\)
3240.2.q.r \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-7q^{19}+\cdots\)
3240.2.q.s \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-3q^{17}-q^{19}+\cdots\)
3240.2.q.t \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.u \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
3240.2.q.v \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.w \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.x \(2\) \(25.872\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
3240.2.q.y \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-2\) \(-1\) \(q+\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots\)
3240.2.q.z \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(0\) \(0\) \(-2\) \(-1\) \(q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
3240.2.q.ba \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-2\) \(-1\) \(q+(-1+\beta _{1})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots\)
3240.2.q.bb \(4\) \(25.872\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(2\) \(q+(-1+\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
3240.2.q.bc \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(0\) \(0\) \(2\) \(-1\) \(q+(1-\beta _{2})q^{5}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
3240.2.q.bd \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(2\) \(-1\) \(q+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots\)
3240.2.q.be \(4\) \(25.872\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(2\) \(-1\) \(q-\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)
3240.2.q.bf \(4\) \(25.872\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(2\) \(q+(1-\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)
3240.2.q.bg \(8\) \(25.872\) 8.0.3887771904.9 None \(0\) \(0\) \(-4\) \(-2\) \(q-\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}-\beta _{7})q^{7}+\cdots\)
3240.2.q.bh \(8\) \(25.872\) 8.0.3887771904.9 None \(0\) \(0\) \(4\) \(-2\) \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}-\beta _{7})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)