Properties

Label 2156.2.a
Level $2156$
Weight $2$
Character orbit 2156.a
Rep. character $\chi_{2156}(1,\cdot)$
Character field $\Q$
Dimension $33$
Newform subspaces $13$
Sturm bound $672$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(672\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2156))\).

Total New Old
Modular forms 360 33 327
Cusp forms 313 33 280
Eisenstein series 47 0 47

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

\(2\)\(7\)\(11\)FrickeDim
\(-\)\(+\)\(+\)$-$\(9\)
\(-\)\(+\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)$+$\(8\)
\(-\)\(-\)\(-\)$-$\(11\)
Plus space\(+\)\(13\)
Minus space\(-\)\(20\)

Trace form

\( 33 q + q^{3} + q^{5} + 34 q^{9} + O(q^{10}) \) \( 33 q + q^{3} + q^{5} + 34 q^{9} - q^{11} - 8 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + 5 q^{23} + 20 q^{25} + 7 q^{27} - 8 q^{29} - 3 q^{31} + 3 q^{33} + 23 q^{37} + 48 q^{39} + 42 q^{43} + 14 q^{45} + 20 q^{47} + 30 q^{51} - 58 q^{53} + 3 q^{55} + 16 q^{57} + 19 q^{59} - 4 q^{61} - 32 q^{65} + 31 q^{67} + 9 q^{69} - 5 q^{71} + 12 q^{73} + 40 q^{75} + 42 q^{79} + 65 q^{81} + 10 q^{83} - 42 q^{85} - 12 q^{87} + 3 q^{89} + 45 q^{93} + 24 q^{95} - 19 q^{97} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2156))\) 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 7 11
2156.2.a.a 2156.a 1.a $1$ $17.216$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{9}-q^{11}+4q^{13}+\cdots\)
2156.2.a.b 2156.a 1.a $1$ $17.216$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots\)
2156.2.a.c 2156.a 1.a $2$ $17.216$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+3q^{9}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
2156.2.a.d 2156.a 1.a $2$ $17.216$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3q^{9}+q^{11}-3\beta q^{13}-\beta q^{17}+\cdots\)
2156.2.a.e 2156.a 1.a $2$ $17.216$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{9}-q^{11}-\beta q^{13}-5\beta q^{17}+\cdots\)
2156.2.a.f 2156.a 1.a $2$ $17.216$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+\beta q^{5}+5q^{9}-q^{11}-\beta q^{13}+\cdots\)
2156.2.a.g 2156.a 1.a $3$ $17.216$ 3.3.257.1 None \(0\) \(-3\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(1+\cdots)q^{9}+\cdots\)
2156.2.a.h 2156.a 1.a $3$ $17.216$ 3.3.321.1 None \(0\) \(-1\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}-2\beta _{2})q^{9}+\cdots\)
2156.2.a.i 2156.a 1.a $3$ $17.216$ 3.3.321.1 None \(0\) \(1\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2156.2.a.j 2156.a 1.a $3$ $17.216$ 3.3.1016.1 None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
2156.2.a.k 2156.a 1.a $3$ $17.216$ 3.3.257.1 None \(0\) \(3\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2156.2.a.l 2156.a 1.a $4$ $17.216$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2156.2.a.m 2156.a 1.a $4$ $17.216$ 4.4.301088.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(4+\beta _{3})q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2156))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)