Properties

Label 1014.2.i
Level $1014$
Weight $2$
Character orbit 1014.i
Rep. character $\chi_{1014}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $8$
Sturm bound $364$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(364\)
Trace bound: \(10\)
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 48 372
Cusp forms 308 48 260
Eisenstein series 112 0 112

Trace form

\( 48q + 24q^{4} - 24q^{9} + O(q^{10}) \) \( 48q + 24q^{4} - 24q^{9} - 4q^{10} + 24q^{14} + 12q^{15} - 24q^{16} + 12q^{17} - 4q^{22} + 16q^{23} - 72q^{25} - 20q^{29} - 4q^{30} - 12q^{33} - 24q^{35} + 24q^{36} + 12q^{37} - 8q^{38} - 8q^{40} - 48q^{41} + 4q^{42} + 8q^{43} + 36q^{49} - 24q^{50} - 32q^{51} + 24q^{53} - 8q^{55} + 12q^{56} + 12q^{58} + 48q^{59} + 20q^{62} - 48q^{64} - 24q^{66} + 48q^{67} - 12q^{68} + 4q^{69} - 24q^{71} + 8q^{74} - 8q^{75} + 32q^{77} + 72q^{79} - 24q^{81} + 8q^{82} + 12q^{84} - 36q^{85} + 4q^{88} + 24q^{89} + 8q^{90} + 32q^{92} + 24q^{93} - 8q^{94} - 8q^{95} - 24q^{98} + O(q^{100}) \)

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.i.a \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-6\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.b \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.c \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.d \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.e \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.f \(4\) \(8.097\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.g \(12\) \(8.097\) 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{10}q^{2}-\beta _{7}q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.i.h \(12\) \(8.097\) 12.0.\(\cdots\).1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(1-\beta _{7})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)