Properties

Label 3528.2.s
Level $3528$
Weight $2$
Character orbit 3528.s
Rep. character $\chi_{3528}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $100$
Newform subspaces $39$
Sturm bound $1344$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 39 \)
Sturm bound: \(1344\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 1472 100 1372
Cusp forms 1216 100 1116
Eisenstein series 256 0 256

Trace form

\( 100 q + 2 q^{5} + O(q^{10}) \) \( 100 q + 2 q^{5} + 2 q^{11} + 6 q^{17} + 10 q^{19} + 2 q^{23} - 36 q^{25} - 16 q^{29} - 6 q^{31} + 6 q^{37} - 16 q^{43} - 6 q^{47} + 2 q^{53} - 4 q^{55} - 18 q^{59} - 10 q^{61} - 12 q^{65} + 2 q^{67} + 80 q^{71} - 22 q^{73} + 10 q^{79} + 56 q^{83} + 36 q^{85} + 34 q^{89} + 50 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3528.2.s.a 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.a.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{17}+2\zeta_{6}q^{19}+\cdots\)
3528.2.s.b 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.s.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+3q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
3528.2.s.c 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.d \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.d 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.q.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+3q^{13}+\cdots\)
3528.2.s.e 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.f 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.g 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}-6q^{13}+(2-2\zeta_{6})q^{17}+\cdots\)
3528.2.s.h 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.a.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+2q^{13}+(-6+6\zeta_{6})q^{17}+\cdots\)
3528.2.s.i 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.j 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 24.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.k 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.d \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.l 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.s.b \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.m 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 1176.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-4q^{13}+(-4+4\zeta_{6})q^{17}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.n 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 1176.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4q^{13}+(4-4\zeta_{6})q^{17}+4\zeta_{6}q^{19}+\cdots\)
3528.2.s.o 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.i.a \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.p 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.q.a \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}-4q^{13}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.q 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.i.b \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}+6q^{13}+(5+\cdots)q^{17}+\cdots\)
3528.2.s.r 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.s.b \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-2q^{13}+(-6+\cdots)q^{17}+\cdots\)
3528.2.s.s 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.d \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.t 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.u 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.v 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.a.b \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}-2q^{13}+(6-6\zeta_{6})q^{17}+\cdots\)
3528.2.s.w 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 168.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+6q^{13}+(-2+2\zeta_{6})q^{17}+\cdots\)
3528.2.s.x 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.y 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 24.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.z 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.a.d \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.ba 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 56.2.a.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{17}-2\zeta_{6}q^{19}+\cdots\)
3528.2.s.bb 3528.s 7.c $2$ $28.171$ \(\Q(\sqrt{-3}) \) None 504.2.s.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+3q^{13}+(-4+4\zeta_{6})q^{17}+\cdots\)
3528.2.s.bc 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1176.2.a.l \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(-2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bd 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1176.2.a.j \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.be 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 392.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+4\beta _{2}q^{11}+\beta _{3}q^{13}+(2\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bf 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 3528.2.a.bf \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+2\beta _{2}q^{11}+2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bg 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 3528.2.a.bg \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bh 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 3528.2.a.bg \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}-\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bi 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 3528.2.a.bf \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}-2\beta _{2}q^{11}-2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bj 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 392.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{5}-6\beta _{2}q^{11}+4\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bk 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None 168.2.q.c \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{5}+(-\beta _{2}+\beta _{3})q^{11}+(-3+\beta _{2}+\cdots)q^{13}+\cdots\)
3528.2.s.bl 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1176.2.a.l \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bm 3528.s 7.c $4$ $28.171$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1176.2.a.j \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)