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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3528.2.s.a \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{17}+2\zeta_{6}q^{19}+\cdots\)
3528.2.s.b \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-4\zeta_{6}q^{5}+3q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
3528.2.s.c \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.d \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+3q^{13}+\cdots\)
3528.2.s.e \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.f \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.g \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}-6q^{13}+(2-2\zeta_{6})q^{17}+\cdots\)
3528.2.s.h \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+2q^{13}+(-6+6\zeta_{6})q^{17}+\cdots\)
3528.2.s.i \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.j \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.k \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.l \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.m \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4q^{13}+(-4+4\zeta_{6})q^{17}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.n \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{13}+(4-4\zeta_{6})q^{17}+4\zeta_{6}q^{19}+\cdots\)
3528.2.s.o \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.p \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}-4q^{13}-4\zeta_{6}q^{19}+\cdots\)
3528.2.s.q \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{11}+6q^{13}+(5+\cdots)q^{17}+\cdots\)
3528.2.s.r \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-2q^{13}+(-6+\cdots)q^{17}+\cdots\)
3528.2.s.s \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(-6+6\zeta_{6})q^{11}+6q^{13}+\cdots\)
3528.2.s.t \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.u \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}-2q^{13}+\cdots\)
3528.2.s.v \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}-2q^{13}+(6-6\zeta_{6})q^{17}+\cdots\)
3528.2.s.w \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+6q^{13}+(-2+2\zeta_{6})q^{17}+\cdots\)
3528.2.s.x \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.y \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2q^{13}+\cdots\)
3528.2.s.z \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(6-6\zeta_{6})q^{11}-6q^{13}+\cdots\)
3528.2.s.ba \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(0\) \(q+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{17}-2\zeta_{6}q^{19}+\cdots\)
3528.2.s.bb \(2\) \(28.171\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(0\) \(q+4\zeta_{6}q^{5}+3q^{13}+(-4+4\zeta_{6})q^{17}+\cdots\)
3528.2.s.bc \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(-2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bd \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.be \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+4\beta _{2}q^{11}+\beta _{3}q^{13}+(2\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bf \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+2\beta _{2}q^{11}+2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bg \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bh \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{3}q^{13}+(\beta _{1}+\beta _{3})q^{17}+\cdots\)
3528.2.s.bi \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-2\beta _{2}q^{11}-2\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bj \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{5}-6\beta _{2}q^{11}+4\beta _{3}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
3528.2.s.bk \(4\) \(28.171\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(1\) \(0\) \(q+\beta _{3}q^{5}+(-\beta _{2}+\beta _{3})q^{11}+(-3+\beta _{2}+\cdots)q^{13}+\cdots\)
3528.2.s.bl \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(4\) \(0\) \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots\)
3528.2.s.bm \(4\) \(28.171\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(4\) \(0\) \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)

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

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