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Properties

Label 2028.2.q
Level $2028$
Weight $2$
Character orbit 2028.q
Rep. character $\chi_{2028}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $50$
Newform subspaces $10$
Sturm bound $728$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2028.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(728\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2028, [\chi])\).

Total New Old
Modular forms 812 50 762
Cusp forms 644 50 594
Eisenstein series 168 0 168

Trace form

\( 50 q + q^{3} - 3 q^{7} - 25 q^{9} + O(q^{10}) \) \( 50 q + q^{3} - 3 q^{7} - 25 q^{9} - 18 q^{11} - 6 q^{15} + 6 q^{17} + 18 q^{19} - 2 q^{23} - 26 q^{25} - 2 q^{27} + 4 q^{29} + 6 q^{33} + 18 q^{35} - 6 q^{37} + 6 q^{41} - 15 q^{43} + 14 q^{49} + 16 q^{51} + 36 q^{53} + 4 q^{55} - 6 q^{59} - q^{61} + 3 q^{63} - 21 q^{67} - 14 q^{69} - 6 q^{71} - 15 q^{75} - 28 q^{77} - 22 q^{79} - 25 q^{81} + 54 q^{85} - 18 q^{87} - 12 q^{89} - 15 q^{93} + 4 q^{95} - 39 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2028.2.q.a 2028.q 13.e $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots\)
2028.2.q.b 2028.q 13.e $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.c 2028.q 13.e $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.d 2028.q 13.e $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
2028.2.q.e 2028.q 13.e $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}^{3}q^{5}-2\zeta_{12}q^{7}+\cdots\)
2028.2.q.f 2028.q 13.e $4$ $16.194$ \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(-2\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2028.2.q.g 2028.q 13.e $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
2028.2.q.h 2028.q 13.e $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
2028.2.q.i 2028.q 13.e $12$ $16.194$ 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{7})q^{3}+(-2\beta _{2}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
2028.2.q.j 2028.q 13.e $12$ $16.194$ 12.0.\(\cdots\).1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{7}q^{3}+(-\beta _{2}-\beta _{8}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)