Properties

Label 1840.2.a
Level $1840$
Weight $2$
Character orbit 1840.a
Rep. character $\chi_{1840}(1,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $22$
Sturm bound $576$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(576\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1840))\).

Total New Old
Modular forms 300 44 256
Cusp forms 277 44 233
Eisenstein series 23 0 23

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

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(-\)$-$\(7\)
\(+\)\(-\)\(+\)$-$\(7\)
\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(7\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(7\)
Plus space\(+\)\(19\)
Minus space\(-\)\(25\)

Trace form

\( 44 q - 4 q^{3} - 8 q^{7} + 52 q^{9} + O(q^{10}) \) \( 44 q - 4 q^{3} - 8 q^{7} + 52 q^{9} + 8 q^{17} - 8 q^{19} + 6 q^{23} + 44 q^{25} - 4 q^{27} - 32 q^{31} - 12 q^{35} - 20 q^{39} - 8 q^{41} - 32 q^{43} + 20 q^{47} + 28 q^{49} + 16 q^{51} + 16 q^{53} + 8 q^{55} - 16 q^{57} + 28 q^{59} + 16 q^{61} + 8 q^{63} - 8 q^{67} - 8 q^{71} + 8 q^{73} - 4 q^{75} + 16 q^{77} - 8 q^{79} + 60 q^{81} + 40 q^{83} + 36 q^{87} + 8 q^{89} + 24 q^{91} - 24 q^{93} + 16 q^{95} + 8 q^{97} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
1840.2.a.a 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(-3\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}-2q^{7}+6q^{9}-3q^{13}+\cdots\)
1840.2.a.b 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{13}+q^{15}+\cdots\)
1840.2.a.c 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}-2q^{9}+6q^{11}+\cdots\)
1840.2.a.d 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
1840.2.a.e 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-6q^{11}+6q^{13}+\cdots\)
1840.2.a.f 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
1840.2.a.g 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}-2q^{11}-5q^{13}+\cdots\)
1840.2.a.h 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1840.2.a.i 1840.a 1.a $1$ $14.692$ \(\Q\) None \(0\) \(3\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+2q^{7}+6q^{9}+q^{13}+\cdots\)
1840.2.a.j 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(2\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots\)
1840.2.a.k 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}-2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
1840.2.a.l 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1840.2.a.m 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.n 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
1840.2.a.o 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.p 1840.a 1.a $2$ $14.692$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots\)
1840.2.a.q 1840.a 1.a $3$ $14.692$ 3.3.229.1 None \(0\) \(-2\) \(3\) \(-7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
1840.2.a.r 1840.a 1.a $3$ $14.692$ 3.3.1101.1 None \(0\) \(-1\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
1840.2.a.s 1840.a 1.a $3$ $14.692$ 3.3.2597.1 None \(0\) \(-1\) \(3\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
1840.2.a.t 1840.a 1.a $3$ $14.692$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1840.2.a.u 1840.a 1.a $4$ $14.692$ 4.4.15317.1 None \(0\) \(2\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(1+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
1840.2.a.v 1840.a 1.a $5$ $14.692$ 5.5.13955077.1 None \(0\) \(0\) \(-5\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)