Properties

Label 4334.2.a
Level $4334$
Weight $2$
Character orbit 4334.a
Rep. character $\chi_{4334}(1,\cdot)$
Character field $\Q$
Dimension $165$
Newform subspaces $8$
Sturm bound $1188$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1188\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4334))\).

Total New Old
Modular forms 598 165 433
Cusp forms 591 165 426
Eisenstein series 7 0 7

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

\(2\)\(11\)\(197\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(24\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(+\)\(17\)
\(-\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(26\)
Plus space\(+\)\(64\)
Minus space\(-\)\(101\)

Trace form

\( 165 q - q^{2} + 4 q^{3} + 165 q^{4} + 2 q^{5} + 4 q^{6} + 8 q^{7} - q^{8} + 173 q^{9} + O(q^{10}) \) \( 165 q - q^{2} + 4 q^{3} + 165 q^{4} + 2 q^{5} + 4 q^{6} + 8 q^{7} - q^{8} + 173 q^{9} - 6 q^{10} + q^{11} + 4 q^{12} + 2 q^{13} + 8 q^{14} + 165 q^{16} - 10 q^{17} + 3 q^{18} + 20 q^{19} + 2 q^{20} + 8 q^{21} - q^{22} + 20 q^{23} + 4 q^{24} + 179 q^{25} - 14 q^{26} - 8 q^{27} + 8 q^{28} + 18 q^{29} + 28 q^{31} - q^{32} - 18 q^{34} - 16 q^{35} + 173 q^{36} + 14 q^{37} - 8 q^{38} + 24 q^{39} - 6 q^{40} - 18 q^{41} - 8 q^{42} + 4 q^{43} + q^{44} + 2 q^{45} + 28 q^{47} + 4 q^{48} + 197 q^{49} - 15 q^{50} - 32 q^{51} + 2 q^{52} - 34 q^{53} + 16 q^{54} + 6 q^{55} + 8 q^{56} - 26 q^{58} - 8 q^{59} + 34 q^{61} - 24 q^{62} - 8 q^{63} + 165 q^{64} + 4 q^{65} + 4 q^{66} + 28 q^{67} - 10 q^{68} - 40 q^{69} + 24 q^{70} - 12 q^{71} + 3 q^{72} + 38 q^{73} - 6 q^{74} + 20 q^{75} + 20 q^{76} + 16 q^{78} + 48 q^{79} + 2 q^{80} + 205 q^{81} - 2 q^{82} - 20 q^{83} + 8 q^{84} - 28 q^{85} + 16 q^{86} + 32 q^{87} - q^{88} - 14 q^{89} + 10 q^{90} + 16 q^{91} + 20 q^{92} + 32 q^{93} + 32 q^{94} - 32 q^{95} + 4 q^{96} - 70 q^{97} + 7 q^{98} + 13 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\) 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 11 197
4334.2.a.a 4334.a 1.a $15$ $34.607$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 4334.2.a.a \(-15\) \(-1\) \(-7\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
4334.2.a.b 4334.a 1.a $15$ $34.607$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 4334.2.a.b \(15\) \(-9\) \(-11\) \(-11\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
4334.2.a.c 4334.a 1.a $17$ $34.607$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 4334.2.a.c \(-17\) \(5\) \(6\) \(-9\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
4334.2.a.d 4334.a 1.a $17$ $34.607$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 4334.2.a.d \(17\) \(-7\) \(-4\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots\)
4334.2.a.e 4334.a 1.a $24$ $34.607$ None 4334.2.a.e \(-24\) \(-4\) \(-4\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$
4334.2.a.f 4334.a 1.a $24$ $34.607$ None 4334.2.a.f \(24\) \(8\) \(0\) \(11\) $-$ $+$ $+$ $\mathrm{SU}(2)$
4334.2.a.g 4334.a 1.a $26$ $34.607$ None 4334.2.a.g \(26\) \(12\) \(13\) \(13\) $-$ $-$ $-$ $\mathrm{SU}(2)$
4334.2.a.h 4334.a 1.a $27$ $34.607$ None 4334.2.a.h \(-27\) \(0\) \(9\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4334)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(197))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(394))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2167))\)\(^{\oplus 2}\)