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Properties

Label 2842.2.a
Level $2842$
Weight $2$
Character orbit 2842.a
Rep. character $\chi_{2842}(1,\cdot)$
Character field $\Q$
Dimension $97$
Newform subspaces $29$
Sturm bound $840$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(840\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2842))\).

Total New Old
Modular forms 436 97 339
Cusp forms 405 97 308
Eisenstein series 31 0 31

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

\(2\)\(7\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(16\)
Plus space\(+\)\(45\)
Minus space\(-\)\(52\)

Trace form

\( 97 q - q^{2} - 4 q^{3} + 97 q^{4} - 2 q^{6} - q^{8} + 95 q^{9} + O(q^{10}) \) \( 97 q - q^{2} - 4 q^{3} + 97 q^{4} - 2 q^{6} - q^{8} + 95 q^{9} + 2 q^{10} - 4 q^{12} + 4 q^{13} + 97 q^{16} + 2 q^{17} + 11 q^{18} + 16 q^{19} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 105 q^{25} + 18 q^{26} - 4 q^{27} - 3 q^{29} + 22 q^{30} - q^{32} + 14 q^{33} - 6 q^{34} + 95 q^{36} - 46 q^{37} - 12 q^{38} - 24 q^{39} + 2 q^{40} - 18 q^{41} - 32 q^{43} + 14 q^{45} + 4 q^{46} - 16 q^{47} - 4 q^{48} + 9 q^{50} + 4 q^{51} + 4 q^{52} + 8 q^{53} - 26 q^{54} + 8 q^{55} - 8 q^{57} - q^{58} - 56 q^{59} + 42 q^{61} + 10 q^{62} + 97 q^{64} + 42 q^{65} + 16 q^{66} - 20 q^{67} + 2 q^{68} + 20 q^{69} - 8 q^{71} + 11 q^{72} + 38 q^{73} + 18 q^{74} + 48 q^{75} + 16 q^{76} + 34 q^{78} - 8 q^{79} + 97 q^{81} + 10 q^{82} + 8 q^{83} + 56 q^{85} + 10 q^{86} + 2 q^{88} + 6 q^{89} + 62 q^{90} + 4 q^{92} + 50 q^{93} + 26 q^{94} - 24 q^{95} - 2 q^{96} - 2 q^{97} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2842))\) 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 29
2842.2.a.a 2842.a 1.a $1$ $22.693$ \(\Q\) None 406.2.a.c \(-1\) \(-2\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
2842.2.a.b 2842.a 1.a $1$ $22.693$ \(\Q\) None 406.2.a.b \(-1\) \(-1\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
2842.2.a.c 2842.a 1.a $1$ $22.693$ \(\Q\) None 406.2.a.a \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-3q^{9}-4q^{11}+q^{16}+\cdots\)
2842.2.a.d 2842.a 1.a $1$ $22.693$ \(\Q\) None 58.2.a.a \(-1\) \(3\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+3q^{5}-3q^{6}-q^{8}+\cdots\)
2842.2.a.e 2842.a 1.a $1$ $22.693$ \(\Q\) None 58.2.a.b \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
2842.2.a.f 2842.a 1.a $1$ $22.693$ \(\Q\) None 406.2.a.d \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
2842.2.a.g 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.g \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}-q^{8}-3q^{9}+\beta q^{10}+\cdots\)
2842.2.a.h 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.h \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2\beta q^{3}+q^{4}-2\beta q^{6}-q^{8}+\cdots\)
2842.2.a.i 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{3}) \) None 406.2.a.e \(2\) \(-4\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+(-1-\beta )q^{5}-2q^{6}+\cdots\)
2842.2.a.j 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.j \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}-3q^{9}+\beta q^{10}+\cdots\)
2842.2.a.k 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.k \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
2842.2.a.l 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.l \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}+\beta q^{6}+\cdots\)
2842.2.a.m 2842.a 1.a $2$ $22.693$ \(\Q(\sqrt{2}) \) None 2842.2.a.m \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2\beta q^{3}+q^{4}-2\beta q^{5}+2\beta q^{6}+\cdots\)
2842.2.a.n 2842.a 1.a $3$ $22.693$ 3.3.568.1 None 406.2.a.f \(-3\) \(-1\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
2842.2.a.o 2842.a 1.a $4$ $22.693$ \(\Q(\sqrt{2}, \sqrt{13})\) None 2842.2.a.o \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
2842.2.a.p 2842.a 1.a $4$ $22.693$ 4.4.9248.1 None 2842.2.a.p \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{3}q^{6}+\cdots\)
2842.2.a.q 2842.a 1.a $4$ $22.693$ \(\Q(\zeta_{24})^+\) None 2842.2.a.q \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(2\beta _{1}+\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
2842.2.a.r 2842.a 1.a $4$ $22.693$ 4.4.11348.1 None 406.2.a.g \(4\) \(-1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
2842.2.a.s 2842.a 1.a $5$ $22.693$ 5.5.369849.1 None 406.2.e.c \(-5\) \(-3\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
2842.2.a.t 2842.a 1.a $5$ $22.693$ 5.5.974241.1 None 406.2.e.d \(-5\) \(-3\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{4})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
2842.2.a.u 2842.a 1.a $5$ $22.693$ 5.5.974241.1 None 406.2.e.d \(-5\) \(3\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2842.2.a.v 2842.a 1.a $5$ $22.693$ 5.5.369849.1 None 406.2.e.c \(-5\) \(3\) \(5\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
2842.2.a.w 2842.a 1.a $5$ $22.693$ 5.5.345065.1 None 406.2.e.b \(5\) \(-3\) \(-7\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
2842.2.a.x 2842.a 1.a $5$ $22.693$ 5.5.1019601.1 None 406.2.e.a \(5\) \(-3\) \(-7\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
2842.2.a.y 2842.a 1.a $5$ $22.693$ 5.5.345065.1 None 406.2.e.b \(5\) \(3\) \(7\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(2+\beta _{2}+\beta _{4})q^{5}+\cdots\)
2842.2.a.z 2842.a 1.a $5$ $22.693$ 5.5.1019601.1 None 406.2.e.a \(5\) \(3\) \(7\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1+\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2842.2.a.ba 2842.a 1.a $6$ $22.693$ 6.6.52756992.1 None 2842.2.a.ba \(-6\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
2842.2.a.bb 2842.a 1.a $6$ $22.693$ 6.6.401917952.1 None 2842.2.a.bb \(6\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2842.2.a.bc 2842.a 1.a $6$ $22.693$ 6.6.373409792.1 None 2842.2.a.bc \(6\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2842))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2842)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(406))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1421))\)\(^{\oplus 2}\)