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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3240.2.q.a 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 120.2.a.a \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.b 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.e \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
3240.2.q.c 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.f \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
3240.2.q.d 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 360.2.a.c \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.e 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.d \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+3q^{17}+\cdots\)
3240.2.q.f 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 3240.2.a.c \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{11}-7q^{19}+6\zeta_{6}q^{23}+\cdots\)
3240.2.q.g 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 120.2.a.b \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-6\zeta_{6}q^{13}+\cdots\)
3240.2.q.h 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.c \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.i 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.b \(0\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.j 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 3240.2.a.a \(0\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
3240.2.q.k 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 40.2.a.a \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
3240.2.q.l 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.a \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
3240.2.q.m 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 120.2.a.a \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.n 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 360.2.a.c \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.o 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.f \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
3240.2.q.p 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.e \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
3240.2.q.q 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 120.2.a.b \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}-6\zeta_{6}q^{13}+\cdots\)
3240.2.q.r 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 3240.2.a.c \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-7q^{19}+\cdots\)
3240.2.q.s 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.d \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-3q^{17}-q^{19}+\cdots\)
3240.2.q.t 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.c \(0\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.u 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 3240.2.a.a \(0\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
3240.2.q.v 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.b \(0\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+6\zeta_{6}q^{13}+\cdots\)
3240.2.q.w 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 1080.2.a.a \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
3240.2.q.x 3240.q 9.c $2$ $25.872$ \(\Q(\sqrt{-3}) \) None 40.2.a.a \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
3240.2.q.y 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 3240.2.a.h \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots\)
3240.2.q.z 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{73})\) None 1080.2.a.m \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
3240.2.q.ba 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 3240.2.a.i \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots\)
3240.2.q.bb 3240.q 9.c $4$ $25.872$ \(\Q(\zeta_{12})\) None 3240.2.a.g \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
3240.2.q.bc 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{73})\) None 1080.2.a.m \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{5}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
3240.2.q.bd 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 3240.2.a.i \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots\)
3240.2.q.be 3240.q 9.c $4$ $25.872$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 3240.2.a.h \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)
3240.2.q.bf 3240.q 9.c $4$ $25.872$ \(\Q(\zeta_{12})\) None 3240.2.a.g \(0\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)
3240.2.q.bg 3240.q 9.c $8$ $25.872$ 8.0.3887771904.9 None 3240.2.a.t \(0\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}-\beta _{7})q^{7}+\cdots\)
3240.2.q.bh 3240.q 9.c $8$ $25.872$ 8.0.3887771904.9 None 3240.2.a.t \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}-\beta _{7})q^{7}+\cdots\)

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

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