Properties

Label 1014.2.e
Level $1014$
Weight $2$
Character orbit 1014.e
Rep. character $\chi_{1014}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $52$
Newform subspaces $14$
Sturm bound $364$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(364\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

Total New Old
Modular forms 420 52 368
Cusp forms 308 52 256
Eisenstein series 112 0 112

Trace form

\( 52q - 2q^{2} - 26q^{4} - 4q^{5} + 4q^{8} - 26q^{9} + O(q^{10}) \) \( 52q - 2q^{2} - 26q^{4} - 4q^{5} + 4q^{8} - 26q^{9} - 2q^{10} + 8q^{11} + 8q^{14} + 4q^{15} - 26q^{16} - 2q^{17} + 4q^{18} + 2q^{20} - 8q^{21} - 12q^{22} - 8q^{23} + 72q^{25} - 18q^{29} - 4q^{30} + 16q^{31} - 2q^{32} + 4q^{33} + 4q^{34} - 26q^{36} - 18q^{37} + 8q^{38} + 4q^{40} + 2q^{41} - 4q^{42} - 8q^{43} - 16q^{44} + 2q^{45} - 16q^{47} - 46q^{49} + 32q^{51} + 20q^{53} + 8q^{55} - 4q^{56} - 8q^{57} + 6q^{58} - 8q^{59} - 8q^{60} - 30q^{61} + 4q^{62} + 52q^{64} + 8q^{66} - 8q^{67} - 2q^{68} - 20q^{69} + 16q^{70} - 8q^{71} - 2q^{72} + 52q^{73} + 18q^{74} + 8q^{75} + 56q^{79} + 2q^{80} - 26q^{81} - 6q^{82} + 4q^{84} - 14q^{85} + 8q^{87} - 12q^{88} + 20q^{89} + 4q^{90} + 16q^{92} - 16q^{94} - 8q^{95} + 12q^{97} + 6q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1014.2.e.a \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-6\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.b \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(4\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.c \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-4\) \(4\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.d \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(2\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.e \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.f \(2\) \(8.097\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(4\) \(-4\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.g \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(8\) \(2\) \(q+(-1+\zeta_{12})q^{2}+(-1+\zeta_{12})q^{3}+\cdots\)
1014.2.e.h \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(0\) \(6\) \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.i \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(-8\) \(-2\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.j \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(2\) \(2\) \(0\) \(-6\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.k \(6\) \(8.097\) 6.0.64827.1 None \(-3\) \(-3\) \(-6\) \(-3\) \(q+(-1+\beta _{5})q^{2}+(-1+\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.l \(6\) \(8.097\) 6.0.64827.1 None \(-3\) \(3\) \(2\) \(-9\) \(q+(-1+\beta _{5})q^{2}+(1-\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.m \(6\) \(8.097\) 6.0.64827.1 None \(3\) \(-3\) \(6\) \(3\) \(q+\beta _{5}q^{2}-\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.e.n \(6\) \(8.097\) 6.0.64827.1 None \(3\) \(3\) \(-2\) \(9\) \(q+\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)