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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2028.2.q.a \(2\) \(16.194\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-6\) \(q+(1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots\)
2028.2.q.b \(2\) \(16.194\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.c \(2\) \(16.194\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.d \(4\) \(16.194\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
2028.2.q.e \(4\) \(16.194\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}^{3}q^{5}-2\zeta_{12}q^{7}+\cdots\)
2028.2.q.f \(4\) \(16.194\) \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(-2\) \(0\) \(3\) \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2028.2.q.g \(4\) \(16.194\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
2028.2.q.h \(4\) \(16.194\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
2028.2.q.i \(12\) \(16.194\) 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(0\) \(q+(-1+\beta _{7})q^{3}+(-2\beta _{2}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
2028.2.q.j \(12\) \(16.194\) 12.0.\(\cdots\).1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{7}q^{3}+(-\beta _{2}-\beta _{8}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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