Properties

Label 2028.2.i
Level $2028$
Weight $2$
Character orbit 2028.i
Rep. character $\chi_{2028}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $54$
Newform subspaces $14$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(728\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 812 54 758
Cusp forms 644 54 590
Eisenstein series 168 0 168

Trace form

\( 54 q - q^{3} - 4 q^{5} + q^{7} - 27 q^{9} + O(q^{10}) \) \( 54 q - q^{3} - 4 q^{5} + q^{7} - 27 q^{9} + 2 q^{11} - 2 q^{15} - 8 q^{17} + 4 q^{19} + 2 q^{21} + 10 q^{23} + 50 q^{25} + 2 q^{27} + 6 q^{29} + 2 q^{31} - 2 q^{33} + 6 q^{35} + 10 q^{37} - 4 q^{41} + 5 q^{43} + 2 q^{45} + 20 q^{47} - 34 q^{49} - 16 q^{51} - 16 q^{53} + 8 q^{55} + 8 q^{57} - 2 q^{59} - 5 q^{61} + q^{63} - 7 q^{67} - 2 q^{69} + 10 q^{71} + 14 q^{73} + q^{75} + 12 q^{77} - 42 q^{79} - 27 q^{81} - 24 q^{83} - 8 q^{85} - 10 q^{87} - 16 q^{89} + q^{93} + 4 q^{95} + 13 q^{97} - 4 q^{99} + O(q^{100}) \)

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.i.a 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.b 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.c 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.d 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.e 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-4q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.f 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.g 2028.i 13.c $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(8\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+4q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.h 2028.i 13.c $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots\)
2028.2.i.i 2028.i 13.c $4$ $16.194$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{5}+(-1+\zeta_{12}+\cdots)q^{9}+\cdots\)
2028.2.i.j 2028.i 13.c $6$ $16.194$ 6.0.64827.1 None \(0\) \(-3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{3}+(1-2\beta _{2}+\beta _{3})q^{5}+\cdots\)
2028.2.i.k 2028.i 13.c $6$ $16.194$ 6.0.64827.1 None \(0\) \(-3\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{3}+(-1+2\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
2028.2.i.l 2028.i 13.c $6$ $16.194$ 6.0.64827.1 None \(0\) \(3\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2028.2.i.m 2028.i 13.c $6$ $16.194$ 6.0.64827.1 None \(0\) \(3\) \(4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{1}+2\beta _{4}+\cdots)q^{7}+\cdots\)
2028.2.i.n 2028.i 13.c $8$ $16.194$ 8.0.\(\cdots\).2 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}+(-\beta _{4}+\beta _{5}-\beta _{7})q^{5}+\cdots\)

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

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