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Properties

Label 2828.2.a
Level $2828$
Weight $2$
Character orbit 2828.a
Rep. character $\chi_{2828}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $7$
Sturm bound $816$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2828 = 2^{2} \cdot 7 \cdot 101 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2828.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(816\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2828))\).

Total New Old
Modular forms 414 50 364
Cusp forms 403 50 353
Eisenstein series 11 0 11

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

\(2\)\(7\)\(101\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(14\)
Plus space\(+\)\(22\)
Minus space\(-\)\(28\)

Trace form

\( 50 q - 4 q^{5} + 46 q^{9} + O(q^{10}) \) \( 50 q - 4 q^{5} + 46 q^{9} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 4 q^{21} - 12 q^{23} + 26 q^{25} + 12 q^{27} - 12 q^{31} + 20 q^{33} - 16 q^{37} + 4 q^{39} + 4 q^{43} + 16 q^{45} + 16 q^{47} + 50 q^{49} + 52 q^{51} + 12 q^{53} + 12 q^{55} + 40 q^{57} + 20 q^{59} + 12 q^{61} + 8 q^{65} + 20 q^{67} + 4 q^{69} + 8 q^{73} + 36 q^{75} - 8 q^{77} - 32 q^{79} + 18 q^{81} + 36 q^{83} - 56 q^{85} + 36 q^{87} - 28 q^{89} + 16 q^{93} + 40 q^{95} + 12 q^{97} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2828))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 101
2828.2.a.a 2828.a 1.a $1$ $22.582$ \(\Q\) None 2828.2.a.a \(0\) \(-3\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{7}+6q^{9}+2q^{11}-4q^{13}+\cdots\)
2828.2.a.b 2828.a 1.a $1$ $22.582$ \(\Q\) None 2828.2.a.b \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
2828.2.a.c 2828.a 1.a $2$ $22.582$ \(\Q(\sqrt{5}) \) None 2828.2.a.c \(0\) \(6\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2-3\beta )q^{5}-q^{7}+6q^{9}+(1+\cdots)q^{11}+\cdots\)
2828.2.a.d 2828.a 1.a $10$ $22.582$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 2828.2.a.d \(0\) \(-3\) \(-3\) \(10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{7}q^{3}+(-\beta _{1}+\beta _{3}+\beta _{8})q^{5}+q^{7}+\cdots\)
2828.2.a.e 2828.a 1.a $11$ $22.582$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 2828.2.a.e \(0\) \(-4\) \(1\) \(-11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{9}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
2828.2.a.f 2828.a 1.a $11$ $22.582$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 2828.2.a.f \(0\) \(1\) \(-4\) \(-11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{10}q^{5}-q^{7}+(1+\beta _{6}-\beta _{7}+\cdots)q^{9}+\cdots\)
2828.2.a.g 2828.a 1.a $14$ $22.582$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 2828.2.a.g \(0\) \(4\) \(1\) \(14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2828))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2828)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(101))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(202))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(404))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(707))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1414))\)\(^{\oplus 2}\)