Properties

Label 1368.2.s
Level $1368$
Weight $2$
Character orbit 1368.s
Rep. character $\chi_{1368}(505,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $50$
Newform subspaces $13$
Sturm bound $480$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(480\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 512 50 462
Cusp forms 448 50 398
Eisenstein series 64 0 64

Trace form

\( 50q + 4q^{7} + O(q^{10}) \) \( 50q + 4q^{7} + 2q^{11} + 4q^{17} + q^{19} + 2q^{23} - 21q^{25} - 8q^{29} - 16q^{31} - 12q^{35} + 8q^{37} - 7q^{41} + 6q^{43} - 12q^{47} + 26q^{49} + 4q^{53} - 10q^{55} + 25q^{59} + 52q^{65} - 23q^{67} + 8q^{71} - 15q^{73} - 12q^{77} - 14q^{79} + 42q^{83} - 18q^{85} + 12q^{89} + 16q^{91} - 34q^{95} + 27q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1368.2.s.a \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-4+4\zeta_{6})q^{5}-3q^{11}-2\zeta_{6}q^{13}+\cdots\)
1368.2.s.b \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-10\) \(q+(-2+2\zeta_{6})q^{5}-5q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots\)
1368.2.s.c \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(6\) \(q+(-2+2\zeta_{6})q^{5}+3q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.d \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(6\) \(q+3q^{7}-2q^{11}-\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1368.2.s.e \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-6\) \(q+(2-2\zeta_{6})q^{5}-3q^{7}-5\zeta_{6}q^{13}+(-4+\cdots)q^{17}+\cdots\)
1368.2.s.f \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(6\) \(q+(2-2\zeta_{6})q^{5}+3q^{7}+6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.g \(2\) \(10.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(3-3\zeta_{6})q^{5}+4q^{11}+5\zeta_{6}q^{13}+\cdots\)
1368.2.s.h \(4\) \(10.924\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(-2\) \(8\) \(q+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{3})q^{7}+\cdots\)
1368.2.s.i \(4\) \(10.924\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-3+\beta _{3})q^{11}+\cdots\)
1368.2.s.j \(6\) \(10.924\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(6\) \(q+(-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+(1-\zeta_{18}^{5})q^{7}+\cdots\)
1368.2.s.k \(6\) \(10.924\) 6.0.2696112.1 None \(0\) \(0\) \(1\) \(-4\) \(q+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.l \(8\) \(10.924\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-4\) \(-4\) \(q+(\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.m \(8\) \(10.924\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(4\) \(-4\) \(q+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)