Properties

Label 1260.2.s
Level $1260$
Weight $2$
Character orbit 1260.s
Rep. character $\chi_{1260}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $8$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 624 28 596
Cusp forms 528 28 500
Eisenstein series 96 0 96

Trace form

\( 28q - 2q^{5} + 2q^{7} + O(q^{10}) \) \( 28q - 2q^{5} + 2q^{7} - 16q^{13} - 12q^{17} - 4q^{19} - 6q^{23} - 14q^{25} - 4q^{29} + 20q^{37} + 20q^{41} + 4q^{43} + 16q^{47} + 10q^{49} + 16q^{53} + 8q^{55} - 12q^{59} + 2q^{61} + 14q^{67} - 64q^{71} + 32q^{77} + 12q^{79} + 52q^{83} + 8q^{85} - 6q^{89} - 48q^{91} + 8q^{95} - 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1260.2.s.a \(2\) \(10.061\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-5\) \(q-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1260.2.s.b \(2\) \(10.061\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1260.2.s.c \(2\) \(10.061\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(5\) \(q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1260.2.s.d \(2\) \(10.061\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(5\) \(q+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1260.2.s.e \(4\) \(10.061\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(-2\) \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots\)
1260.2.s.f \(4\) \(10.061\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
1260.2.s.g \(6\) \(10.061\) 6.0.4406832.1 None \(0\) \(0\) \(-3\) \(-1\) \(q+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
1260.2.s.h \(6\) \(10.061\) 6.0.4406832.1 None \(0\) \(0\) \(3\) \(-1\) \(q+(1-\beta _{3})q^{5}-\beta _{4}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)