Properties

Label 1638.2.r
Level $1638$
Weight $2$
Character orbit 1638.r
Rep. character $\chi_{1638}(757,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $68$
Newform subspaces $27$
Sturm bound $672$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 27 \)
Sturm bound: \(672\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 704 68 636
Cusp forms 640 68 572
Eisenstein series 64 0 64

Trace form

\( 68q + 2q^{2} - 34q^{4} + 4q^{5} - 4q^{8} + O(q^{10}) \) \( 68q + 2q^{2} - 34q^{4} + 4q^{5} - 4q^{8} - 2q^{10} - 12q^{11} + 22q^{13} + 8q^{14} - 34q^{16} - 6q^{17} - 16q^{19} - 2q^{20} + 4q^{22} + 40q^{25} + 10q^{26} + 2q^{29} - 24q^{31} + 2q^{32} + 44q^{34} - 2q^{37} - 16q^{38} + 4q^{40} + 18q^{41} + 20q^{43} + 24q^{44} + 12q^{46} - 34q^{49} + 12q^{50} - 8q^{52} + 28q^{53} - 12q^{55} - 4q^{56} - 14q^{58} + 16q^{59} - 14q^{61} + 12q^{62} + 68q^{64} - 26q^{65} + 12q^{67} - 6q^{68} + 8q^{71} - 44q^{73} - 42q^{74} - 16q^{76} + 32q^{77} + 40q^{79} - 2q^{80} - 22q^{82} + 88q^{83} - 22q^{85} - 8q^{86} + 4q^{88} - 28q^{89} + 20q^{91} + 44q^{95} + 20q^{97} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1638.2.r.a \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-8\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{5}-\zeta_{6}q^{7}+\cdots\)
1638.2.r.b \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-8\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.c \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-\zeta_{6}q^{7}+\cdots\)
1638.2.r.d \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.e \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.f \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1638.2.r.g \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1638.2.r.h \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1638.2.r.i \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1638.2.r.j \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}-\zeta_{6}q^{7}+\cdots\)
1638.2.r.k \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.l \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.m \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}-\zeta_{6}q^{7}+\cdots\)
1638.2.r.n \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}-\zeta_{6}q^{7}+\cdots\)
1638.2.r.o \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-6\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.p \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+\cdots\)
1638.2.r.q \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+\cdots\)
1638.2.r.r \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+\cdots\)
1638.2.r.s \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+\cdots\)
1638.2.r.t \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(8\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{5}+\zeta_{6}q^{7}+\cdots\)
1638.2.r.u \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-2\) \(0\) \(8\) \(2\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+2q^{5}+\beta _{1}q^{7}+\cdots\)
1638.2.r.v \(4\) \(13.079\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-8\) \(2\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(-2-\zeta_{12}^{3})q^{5}+\cdots\)
1638.2.r.w \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(2\) \(0\) \(-8\) \(2\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}-2q^{5}+\beta _{1}q^{7}+\cdots\)
1638.2.r.x \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(2\) \(0\) \(-2\) \(-2\) \(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1638.2.r.y \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(0\) \(2\) \(-2\) \(q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1638.2.r.z \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(0\) \(6\) \(2\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
1638.2.r.ba \(4\) \(13.079\) \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(2\) \(0\) \(8\) \(2\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+2q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)