Properties

Label 2028.2.b
Level $2028$
Weight $2$
Character orbit 2028.b
Rep. character $\chi_{2028}(337,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $7$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(728\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 406 24 382
Cusp forms 322 24 298
Eisenstein series 84 0 84

Trace form

\( 24 q + 24 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{9} - 12 q^{17} + 20 q^{23} - 12 q^{25} + 8 q^{29} + 12 q^{35} + 4 q^{43} - 24 q^{49} + 20 q^{51} - 24 q^{53} - 4 q^{55} - 24 q^{61} + 20 q^{69} - 16 q^{75} - 56 q^{77} + 12 q^{79} + 24 q^{81} - 12 q^{87} - 52 q^{95} + O(q^{100}) \)

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.b.a 2028.b 13.b $2$ $16.194$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
2028.2.b.b 2028.b 13.b $2$ $16.194$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
2028.2.b.c 2028.b 13.b $2$ $16.194$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
2028.2.b.d 2028.b 13.b $2$ $16.194$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{7}+q^{9}+6q^{17}-iq^{19}+\cdots\)
2028.2.b.e 2028.b 13.b $4$ $16.194$ \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
2028.2.b.f 2028.b 13.b $6$ $16.194$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(\beta _{3}+\beta _{5})q^{5}+(-2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
2028.2.b.g 2028.b 13.b $6$ $16.194$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{3}-2\beta _{5})q^{7}+\cdots\)

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

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