Properties

Label 4284.2.a
Level $4284$
Weight $2$
Character orbit 4284.a
Rep. character $\chi_{4284}(1,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $22$
Sturm bound $1728$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4284.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1728\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4284))\).

Total New Old
Modular forms 888 40 848
Cusp forms 841 40 801
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.

\(2\)\(3\)\(7\)\(17\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(6\)
\(-\)\(-\)\(+\)\(-\)$-$\(6\)
\(-\)\(-\)\(-\)\(+\)$-$\(6\)
\(-\)\(-\)\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(20\)
Minus space\(-\)\(20\)

Trace form

\( 40 q + 4 q^{5} + O(q^{10}) \) \( 40 q + 4 q^{5} - 4 q^{11} + 4 q^{13} + 4 q^{19} + 28 q^{25} - 4 q^{29} - 4 q^{31} - 4 q^{35} - 8 q^{37} + 4 q^{41} - 4 q^{43} + 24 q^{47} + 40 q^{49} - 20 q^{53} - 12 q^{55} - 8 q^{59} - 28 q^{61} - 72 q^{65} - 4 q^{67} + 32 q^{71} - 12 q^{73} - 20 q^{79} - 28 q^{83} + 8 q^{85} + 48 q^{89} + 4 q^{91} + 4 q^{95} - 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4284))\) 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 3 7 17
4284.2.a.a 4284.a 1.a $1$ $34.208$ \(\Q\) None 4284.2.a.a \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-2q^{11}-6q^{13}-q^{17}+\cdots\)
4284.2.a.b 4284.a 1.a $1$ $34.208$ \(\Q\) None 1428.2.a.c \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{13}+q^{17}-2q^{19}+\cdots\)
4284.2.a.c 4284.a 1.a $1$ $34.208$ \(\Q\) None 1428.2.a.e \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{13}+q^{17}+6q^{19}+\cdots\)
4284.2.a.d 4284.a 1.a $1$ $34.208$ \(\Q\) None 4284.2.a.d \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+2q^{11}+2q^{13}-q^{17}+\cdots\)
4284.2.a.e 4284.a 1.a $1$ $34.208$ \(\Q\) None 1428.2.a.b \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+q^{11}-7q^{13}+q^{17}+\cdots\)
4284.2.a.f 4284.a 1.a $1$ $34.208$ \(\Q\) None 4284.2.a.a \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{11}-6q^{13}+q^{17}+\cdots\)
4284.2.a.g 4284.a 1.a $1$ $34.208$ \(\Q\) None 4284.2.a.d \(0\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{11}+2q^{13}+q^{17}+\cdots\)
4284.2.a.h 4284.a 1.a $1$ $34.208$ \(\Q\) None 1428.2.a.a \(0\) \(0\) \(3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}+5q^{11}+q^{13}+q^{17}+\cdots\)
4284.2.a.i 4284.a 1.a $1$ $34.208$ \(\Q\) None 1428.2.a.d \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
4284.2.a.j 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{17}) \) None 1428.2.a.i \(0\) \(0\) \(-3\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(-1+\beta )q^{11}+\cdots\)
4284.2.a.k 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{10}) \) None 1428.2.a.h \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}-3q^{11}+(3-\beta )q^{13}+\cdots\)
4284.2.a.l 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{13}) \) None 476.2.a.c \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-q^{7}-4q^{11}+(-2+2\beta )q^{13}+\cdots\)
4284.2.a.m 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{5}) \) None 476.2.a.b \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(2+2\beta )q^{11}-2\beta q^{13}+\cdots\)
4284.2.a.n 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{13}) \) None 476.2.a.d \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(2+2\beta )q^{13}-q^{17}+\cdots\)
4284.2.a.o 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{2}) \) None 1428.2.a.g \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(1-2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
4284.2.a.p 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{13}) \) None 476.2.a.a \(0\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}-2\beta q^{11}+(-2-2\beta )q^{13}+\cdots\)
4284.2.a.q 4284.a 1.a $2$ $34.208$ \(\Q(\sqrt{3}) \) None 1428.2.a.f \(0\) \(0\) \(4\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-q^{7}+(-3-2\beta )q^{11}+\cdots\)
4284.2.a.r 4284.a 1.a $3$ $34.208$ 3.3.3028.1 None 4284.2.a.r \(0\) \(0\) \(-3\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+q^{7}-3q^{11}-\beta _{2}q^{13}+\cdots\)
4284.2.a.s 4284.a 1.a $3$ $34.208$ 3.3.4764.1 None 1428.2.a.j \(0\) \(0\) \(-2\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+q^{7}+(1+\beta _{2})q^{11}+\cdots\)
4284.2.a.t 4284.a 1.a $3$ $34.208$ 3.3.404.1 None 4284.2.a.t \(0\) \(0\) \(-1\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}-q^{7}+(-3+2\beta _{1})q^{11}+(2+\cdots)q^{13}+\cdots\)
4284.2.a.u 4284.a 1.a $3$ $34.208$ 3.3.404.1 None 4284.2.a.t \(0\) \(0\) \(1\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}-q^{7}+(3-2\beta _{1})q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots\)
4284.2.a.v 4284.a 1.a $3$ $34.208$ 3.3.3028.1 None 4284.2.a.r \(0\) \(0\) \(3\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+q^{7}+3q^{11}-\beta _{2}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4284))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4284)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1071))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1428))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2142))\)\(^{\oplus 2}\)