Properties

Label 1840.4.a
Level $1840$
Weight $4$
Character orbit 1840.a
Rep. character $\chi_{1840}(1,\cdot)$
Character field $\Q$
Dimension $132$
Newform subspaces $28$
Sturm bound $1152$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(1152\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1840))\).

Total New Old
Modular forms 876 132 744
Cusp forms 852 132 720
Eisenstein series 24 0 24

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.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(69\)
Minus space\(-\)\(63\)

Trace form

\( 132 q + 12 q^{3} - 72 q^{7} + 1148 q^{9} + O(q^{10}) \) \( 132 q + 12 q^{3} - 72 q^{7} + 1148 q^{9} + 152 q^{17} - 360 q^{19} - 138 q^{23} + 3300 q^{25} + 300 q^{27} + 480 q^{31} + 768 q^{33} + 420 q^{35} + 12 q^{39} + 40 q^{41} - 672 q^{43} - 940 q^{47} + 7188 q^{49} - 1712 q^{51} - 784 q^{53} - 440 q^{55} + 1104 q^{57} + 332 q^{59} - 400 q^{61} - 2552 q^{63} - 1512 q^{67} - 1864 q^{71} - 2088 q^{73} + 300 q^{75} + 368 q^{77} + 504 q^{79} + 8692 q^{81} + 2440 q^{83} - 60 q^{87} + 1880 q^{89} - 7816 q^{91} + 2136 q^{93} - 1520 q^{95} - 1512 q^{97} - 6424 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
1840.4.a.a $1$ $108.564$ \(\Q\) None \(0\) \(-7\) \(5\) \(-20\) $-$ $-$ $+$ \(q-7q^{3}+5q^{5}-20q^{7}+22q^{9}-6q^{11}+\cdots\)
1840.4.a.b $1$ $108.564$ \(\Q\) None \(0\) \(-4\) \(-5\) \(-3\) $-$ $+$ $+$ \(q-4q^{3}-5q^{5}-3q^{7}-11q^{9}+2q^{11}+\cdots\)
1840.4.a.c $1$ $108.564$ \(\Q\) None \(0\) \(-4\) \(-5\) \(32\) $-$ $+$ $+$ \(q-4q^{3}-5q^{5}+2^{5}q^{7}-11q^{9}-40q^{11}+\cdots\)
1840.4.a.d $1$ $108.564$ \(\Q\) None \(0\) \(-1\) \(-5\) \(18\) $-$ $+$ $-$ \(q-q^{3}-5q^{5}+18q^{7}-26q^{9}+2^{5}q^{11}+\cdots\)
1840.4.a.e $1$ $108.564$ \(\Q\) None \(0\) \(1\) \(5\) \(32\) $-$ $-$ $+$ \(q+q^{3}+5q^{5}+2^{5}q^{7}-26q^{9}+30q^{11}+\cdots\)
1840.4.a.f $1$ $108.564$ \(\Q\) None \(0\) \(3\) \(5\) \(2\) $-$ $-$ $-$ \(q+3q^{3}+5q^{5}+2q^{7}-18q^{9}+2^{4}q^{11}+\cdots\)
1840.4.a.g $1$ $108.564$ \(\Q\) None \(0\) \(5\) \(-5\) \(-12\) $-$ $+$ $+$ \(q+5q^{3}-5q^{5}-12q^{7}-2q^{9}-22q^{11}+\cdots\)
1840.4.a.h $2$ $108.564$ \(\Q(\sqrt{109}) \) None \(0\) \(3\) \(10\) \(-1\) $-$ $-$ $-$ \(q+(1+\beta )q^{3}+5q^{5}+(2-5\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.4.a.i $2$ $108.564$ \(\Q(\sqrt{73}) \) None \(0\) \(3\) \(10\) \(17\) $-$ $-$ $-$ \(q+(1+\beta )q^{3}+5q^{5}+(8+\beta )q^{7}+(-8+\cdots)q^{9}+\cdots\)
1840.4.a.j $3$ $108.564$ 3.3.318165.1 None \(0\) \(1\) \(15\) \(-7\) $-$ $-$ $+$ \(q+\beta _{1}q^{3}+5q^{5}+(-1-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
1840.4.a.k $4$ $108.564$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-14\) \(20\) \(-8\) $-$ $-$ $-$ \(q+(-4+\beta _{1})q^{3}+5q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.l $4$ $108.564$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-4\) \(-20\) \(-26\) $-$ $+$ $+$ \(q+(-1+\beta _{1})q^{3}-5q^{5}+(-6+\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.m $4$ $108.564$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(4\) \(-20\) \(1\) $-$ $+$ $-$ \(q+(1-\beta _{1})q^{3}-5q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.4.a.n $5$ $108.564$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-4\) \(-25\) \(3\) $-$ $+$ $-$ \(q+(-1-\beta _{4})q^{3}-5q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+\cdots\)
1840.4.a.o $5$ $108.564$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(3\) \(-25\) \(-8\) $-$ $+$ $-$ \(q+(1-\beta _{1})q^{3}-5q^{5}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
1840.4.a.p $5$ $108.564$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(6\) \(-25\) \(15\) $-$ $+$ $+$ \(q+(1-\beta _{1}+\beta _{3})q^{3}-5q^{5}+(2+3\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.q $5$ $108.564$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(7\) \(25\) \(20\) $-$ $-$ $+$ \(q+(1+\beta _{3})q^{3}+5q^{5}+(5+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1840.4.a.r $6$ $108.564$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-3\) \(-30\) \(-20\) $-$ $+$ $+$ \(q+(-1+\beta _{1})q^{3}-5q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.s $6$ $108.564$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(-30\) \(-28\) $+$ $+$ $-$ \(q-\beta _{1}q^{3}-5q^{5}+(-5-\beta _{2}-\beta _{4})q^{7}+\cdots\)
1840.4.a.t $6$ $108.564$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(1\) \(30\) \(-24\) $-$ $-$ $-$ \(q+\beta _{1}q^{3}+5q^{5}+(-4-\beta _{3}+\beta _{4})q^{7}+\cdots\)
1840.4.a.u $6$ $108.564$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(4\) \(30\) \(14\) $+$ $-$ $+$ \(q+(1-\beta _{1})q^{3}+5q^{5}+(2+\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1840.4.a.v $8$ $108.564$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(40\) \(-11\) $-$ $-$ $+$ \(q+\beta _{3}q^{3}+5q^{5}+(-1+\beta _{3}+\beta _{6})q^{7}+\cdots\)
1840.4.a.w $8$ $108.564$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(6\) \(-40\) \(3\) $+$ $+$ $+$ \(q+(1-\beta _{1})q^{3}-5q^{5}-\beta _{5}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots\)
1840.4.a.x $8$ $108.564$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(12\) \(40\) \(31\) $+$ $-$ $-$ \(q+(2-\beta _{1})q^{3}+5q^{5}+(3+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1840.4.a.y $9$ $108.564$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(45\) \(-25\) $+$ $-$ $+$ \(q-\beta _{1}q^{3}+5q^{5}+(-3+\beta _{3})q^{7}+(7+\cdots)q^{9}+\cdots\)
1840.4.a.z $9$ $108.564$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(-45\) \(-25\) $+$ $+$ $-$ \(q+\beta _{1}q^{3}-5q^{5}+(-3+\beta _{3})q^{7}+(6+\cdots)q^{9}+\cdots\)
1840.4.a.ba $10$ $108.564$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-5\) \(50\) \(-14\) $+$ $-$ $-$ \(q-\beta _{1}q^{3}+5q^{5}+(-1-\beta _{1}+\beta _{6})q^{7}+\cdots\)
1840.4.a.bb $10$ $108.564$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(1\) \(-50\) \(-28\) $+$ $+$ $+$ \(q+\beta _{1}q^{3}-5q^{5}+(-3-\beta _{1}-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1840))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1840)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)