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Properties

Label 2028.2.a
Level $2028$
Weight $2$
Character orbit 2028.a
Rep. character $\chi_{2028}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $13$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(728\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2028))\).

Total New Old
Modular forms 406 26 380
Cusp forms 323 26 297
Eisenstein series 83 0 83

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(13\)FrickeDim
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(7\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(11\)
Minus space\(-\)\(15\)

Trace form

\( 26 q + 4 q^{5} + 26 q^{9} + O(q^{10}) \) \( 26 q + 4 q^{5} + 26 q^{9} + 4 q^{11} - 4 q^{15} + 8 q^{17} - 4 q^{21} - 4 q^{23} + 18 q^{25} + 12 q^{29} + 8 q^{31} - 4 q^{33} - 12 q^{35} - 12 q^{37} + 4 q^{41} - 4 q^{43} + 4 q^{45} + 4 q^{47} + 34 q^{49} + 4 q^{51} + 4 q^{53} - 20 q^{55} - 4 q^{57} - 4 q^{59} + 12 q^{61} + 8 q^{67} - 4 q^{69} - 28 q^{71} - 4 q^{73} + 16 q^{75} + 4 q^{79} + 26 q^{81} - 12 q^{83} + 8 q^{85} + 4 q^{87} + 4 q^{89} - 12 q^{93} - 4 q^{95} + 12 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2028))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13
2028.2.a.a 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
2028.2.a.b 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
2028.2.a.c 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(-1\) \(4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
2028.2.a.d 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(1\) \(-2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
2028.2.a.e 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-6q^{17}-2q^{19}+\cdots\)
2028.2.a.f 2028.a 1.a $1$ $16.194$ \(\Q\) None \(0\) \(1\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
2028.2.a.g 2028.a 1.a $2$ $16.194$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots\)
2028.2.a.h 2028.a 1.a $2$ $16.194$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-2\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
2028.2.a.i 2028.a 1.a $3$ $16.194$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-2\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{2})q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
2028.2.a.j 2028.a 1.a $3$ $16.194$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(-3+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
2028.2.a.k 2028.a 1.a $3$ $16.194$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(0\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(-3+2\beta _{1}+\cdots)q^{7}+\cdots\)
2028.2.a.l 2028.a 1.a $3$ $16.194$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2028.2.a.m 2028.a 1.a $4$ $16.194$ \(\Q(\sqrt{3}, \sqrt{43})\) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)