Properties

Label 4205.2.a
Level $4205$
Weight $2$
Character orbit 4205.a
Rep. character $\chi_{4205}(1,\cdot)$
Character field $\Q$
Dimension $271$
Newform subspaces $26$
Sturm bound $870$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4205 = 5 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4205.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(870\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4205))\).

Total New Old
Modular forms 464 271 193
Cusp forms 405 271 134
Eisenstein series 59 0 59

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

\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(61\)
\(+\)\(-\)\(-\)\(75\)
\(-\)\(+\)\(-\)\(74\)
\(-\)\(-\)\(+\)\(61\)
Plus space\(+\)\(122\)
Minus space\(-\)\(149\)

Trace form

\( 271 q - q^{2} + 4 q^{3} + 273 q^{4} - q^{5} - 4 q^{6} + 4 q^{7} - 9 q^{8} + 275 q^{9} + O(q^{10}) \) \( 271 q - q^{2} + 4 q^{3} + 273 q^{4} - q^{5} - 4 q^{6} + 4 q^{7} - 9 q^{8} + 275 q^{9} + 3 q^{10} + 16 q^{12} + 10 q^{13} + 8 q^{14} + 273 q^{16} + 6 q^{17} + 7 q^{18} + 16 q^{19} + q^{20} - 24 q^{22} - 20 q^{23} + 271 q^{25} + 2 q^{26} - 8 q^{27} - 16 q^{28} + 4 q^{30} + 4 q^{31} - 9 q^{32} + 8 q^{33} + 6 q^{34} - 4 q^{35} + 301 q^{36} - 6 q^{37} + 12 q^{38} - 32 q^{39} + 15 q^{40} + 22 q^{41} - 20 q^{42} + 12 q^{43} - 5 q^{45} - 40 q^{46} - 8 q^{47} + 12 q^{48} + 279 q^{49} - q^{50} - 6 q^{52} - 22 q^{53} - 24 q^{54} + 4 q^{55} + 24 q^{56} - 8 q^{59} + 12 q^{60} + 2 q^{61} - 44 q^{62} - 20 q^{63} + 253 q^{64} + 2 q^{65} + 16 q^{66} - 20 q^{67} + 38 q^{68} - 16 q^{69} - 12 q^{70} - 40 q^{71} + 31 q^{72} + 26 q^{73} + 42 q^{74} + 4 q^{75} - 16 q^{76} - 4 q^{77} + 12 q^{78} - 4 q^{79} + q^{80} + 287 q^{81} - 26 q^{82} - 20 q^{83} + 16 q^{84} + 2 q^{85} - 12 q^{86} - 76 q^{88} - 26 q^{89} - 13 q^{90} + 4 q^{92} - 8 q^{93} - 24 q^{94} + 12 q^{95} - 28 q^{96} + 34 q^{97} - 69 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4205))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 29
4205.2.a.a 4205.a 1.a $1$ $33.577$ \(\Q\) None 145.2.a.a \(1\) \(0\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\)
4205.2.a.b 4205.a 1.a $2$ $33.577$ \(\Q(\sqrt{5}) \) None 4205.2.a.b \(0\) \(-2\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots\)
4205.2.a.c 4205.a 1.a $2$ $33.577$ \(\Q(\sqrt{5}) \) None 4205.2.a.b \(0\) \(2\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots\)
4205.2.a.d 4205.a 1.a $2$ $33.577$ \(\Q(\sqrt{2}) \) None 145.2.a.b \(2\) \(4\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
4205.2.a.e 4205.a 1.a $3$ $33.577$ 3.3.148.1 None 145.2.a.d \(-3\) \(2\) \(-3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
4205.2.a.f 4205.a 1.a $3$ $33.577$ 3.3.148.1 None 145.2.a.c \(-1\) \(-2\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
4205.2.a.g 4205.a 1.a $4$ $33.577$ \(\Q(\zeta_{24})^+\) None 145.2.c.a \(0\) \(0\) \(4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+q^{5}+\cdots\)
4205.2.a.h 4205.a 1.a $5$ $33.577$ 5.5.1586009.1 None 4205.2.a.h \(-1\) \(-2\) \(5\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4205.2.a.i 4205.a 1.a $5$ $33.577$ 5.5.942577.1 None 4205.2.a.i \(-1\) \(2\) \(-5\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
4205.2.a.j 4205.a 1.a $5$ $33.577$ 5.5.942577.1 None 4205.2.a.i \(1\) \(-2\) \(-5\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
4205.2.a.k 4205.a 1.a $5$ $33.577$ 5.5.1586009.1 None 4205.2.a.h \(1\) \(2\) \(5\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4205.2.a.l 4205.a 1.a $6$ $33.577$ 6.6.5516125.1 None 4205.2.a.l \(-1\) \(-1\) \(-6\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
4205.2.a.m 4205.a 1.a $6$ $33.577$ 6.6.66064384.1 None 145.2.c.b \(0\) \(0\) \(-6\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.n 4205.a 1.a $6$ $33.577$ 6.6.5516125.1 None 4205.2.a.l \(1\) \(1\) \(-6\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
4205.2.a.o 4205.a 1.a $8$ $33.577$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4205.2.a.o \(-3\) \(-7\) \(8\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.p 4205.a 1.a $8$ $33.577$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4205.2.a.o \(3\) \(7\) \(8\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.q 4205.a 1.a $12$ $33.577$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 145.2.k.a \(-1\) \(1\) \(-12\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
4205.2.a.r 4205.a 1.a $12$ $33.577$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 145.2.k.a \(1\) \(-1\) \(-12\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
4205.2.a.s 4205.a 1.a $18$ $33.577$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 145.2.k.b \(-1\) \(-1\) \(18\) \(17\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4205.2.a.t 4205.a 1.a $18$ $33.577$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 145.2.k.b \(1\) \(1\) \(18\) \(17\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4205.2.a.u 4205.a 1.a $20$ $33.577$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 4205.2.a.u \(-9\) \(-13\) \(20\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.v 4205.a 1.a $20$ $33.577$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 4205.2.a.v \(-1\) \(-3\) \(-20\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{17}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4205.2.a.w 4205.a 1.a $20$ $33.577$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 4205.2.a.v \(1\) \(3\) \(-20\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{17}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4205.2.a.x 4205.a 1.a $20$ $33.577$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 4205.2.a.u \(9\) \(13\) \(20\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.y 4205.a 1.a $24$ $33.577$ None 145.2.m.a \(0\) \(0\) \(24\) \(-38\) $-$ $-$ $\mathrm{SU}(2)$
4205.2.a.z 4205.a 1.a $36$ $33.577$ None 145.2.m.b \(0\) \(0\) \(-36\) \(14\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4205)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 2}\)