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Properties

Label 2156.4.a
Level $2156$
Weight $4$
Character orbit 2156.a
Rep. character $\chi_{2156}(1,\cdot)$
Character field $\Q$
Dimension $103$
Newform subspaces $15$
Sturm bound $1344$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2156.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(1344\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2156))\).

Total New Old
Modular forms 1032 103 929
Cusp forms 984 103 881
Eisenstein series 48 0 48

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
\(-\)\(+\)\(+\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(+\)\(28\)
\(-\)\(-\)\(+\)\(+\)\(27\)
\(-\)\(-\)\(-\)\(-\)\(24\)
Plus space\(+\)\(55\)
Minus space\(-\)\(48\)

Trace form

\( 103 q - 8 q^{3} - 16 q^{5} + 989 q^{9} + O(q^{10}) \) \( 103 q - 8 q^{3} - 16 q^{5} + 989 q^{9} + 11 q^{11} - 106 q^{13} + 28 q^{15} - 18 q^{17} + 44 q^{19} + 292 q^{23} + 2411 q^{25} - 752 q^{27} + 190 q^{29} - 164 q^{31} + 22 q^{33} - 808 q^{37} - 992 q^{39} - 30 q^{41} - 980 q^{43} - 1242 q^{45} - 616 q^{47} + 592 q^{51} + 1514 q^{53} + 198 q^{55} - 8 q^{57} + 296 q^{59} - 546 q^{61} - 92 q^{65} + 1908 q^{67} + 1454 q^{69} - 2260 q^{71} - 2438 q^{73} - 144 q^{75} + 80 q^{79} + 9087 q^{81} - 604 q^{83} - 2200 q^{85} + 3400 q^{87} - 1968 q^{89} + 350 q^{93} + 2992 q^{95} + 1804 q^{97} + 407 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2156))\) 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 11
2156.4.a.a 2156.a 1.a $1$ $127.208$ \(\Q\) None 308.4.a.b \(0\) \(-4\) \(12\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+12q^{5}-11q^{9}+11q^{11}+\cdots\)
2156.4.a.b 2156.a 1.a $1$ $127.208$ \(\Q\) None 44.4.a.a \(0\) \(5\) \(7\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}+7q^{5}-2q^{9}-11q^{11}-52q^{13}+\cdots\)
2156.4.a.c 2156.a 1.a $1$ $127.208$ \(\Q\) None 308.4.a.a \(0\) \(7\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+7q^{3}+q^{5}+22q^{9}+11q^{11}-12q^{13}+\cdots\)
2156.4.a.d 2156.a 1.a $2$ $127.208$ \(\Q(\sqrt{97}) \) None 44.4.a.b \(0\) \(-9\) \(-11\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{3}+(-6+\beta )q^{5}+(13+9\beta )q^{9}+\cdots\)
2156.4.a.e 2156.a 1.a $3$ $127.208$ 3.3.5925.1 None 308.4.a.c \(0\) \(-5\) \(-9\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(-2-3\beta _{1})q^{5}+(-11+\cdots)q^{9}+\cdots\)
2156.4.a.f 2156.a 1.a $4$ $127.208$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 308.4.a.d \(0\) \(3\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+(-5+\beta _{2})q^{9}+\cdots\)
2156.4.a.g 2156.a 1.a $5$ $127.208$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 308.4.a.e \(0\) \(-5\) \(-15\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-3-\beta _{2})q^{5}+(20+\cdots)q^{9}+\cdots\)
2156.4.a.h 2156.a 1.a $6$ $127.208$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 2156.4.a.h \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(7-\beta _{4}+\cdots)q^{9}+\cdots\)
2156.4.a.i 2156.a 1.a $8$ $127.208$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 2156.4.a.i \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(10+\beta _{1})q^{9}-11q^{11}+\cdots\)
2156.4.a.j 2156.a 1.a $10$ $127.208$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 308.4.i.a \(0\) \(-6\) \(-10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3})q^{5}+(11+\cdots)q^{9}+\cdots\)
2156.4.a.k 2156.a 1.a $10$ $127.208$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 308.4.i.b \(0\) \(-6\) \(10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(11-\beta _{1}+\cdots)q^{9}+\cdots\)
2156.4.a.l 2156.a 1.a $10$ $127.208$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 308.4.i.b \(0\) \(6\) \(-10\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(11-\beta _{1}+\cdots)q^{9}+\cdots\)
2156.4.a.m 2156.a 1.a $10$ $127.208$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 308.4.i.a \(0\) \(6\) \(10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(11-\beta _{1}+\cdots)q^{9}+\cdots\)
2156.4.a.n 2156.a 1.a $14$ $127.208$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 2156.4.a.n \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(9+\beta _{2})q^{9}-11q^{11}+\cdots\)
2156.4.a.o 2156.a 1.a $18$ $127.208$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 2156.4.a.o \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{9}q^{3}+\beta _{10}q^{5}+(13+\beta _{1})q^{9}+11q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2156))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2156)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)