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Properties

Label 1848.2.a
Level $1848$
Weight $2$
Character orbit 1848.a
Rep. character $\chi_{1848}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $21$
Sturm bound $768$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(768\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1848))\).

Total New Old
Modular forms 400 32 368
Cusp forms 369 32 337
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.

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(14\)
Minus space\(-\)\(18\)

Trace form

\( 32 q - 8 q^{5} + 32 q^{9} + O(q^{10}) \) \( 32 q - 8 q^{5} + 32 q^{9} - 8 q^{13} - 8 q^{17} + 8 q^{23} + 32 q^{25} + 8 q^{29} + 8 q^{31} + 24 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} + 32 q^{49} + 8 q^{51} + 8 q^{53} + 16 q^{59} + 8 q^{61} - 16 q^{65} - 24 q^{71} + 8 q^{73} + 32 q^{79} + 32 q^{81} - 32 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} - 16 q^{91} + 8 q^{93} - 32 q^{95} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 11
1848.2.a.a $1$ $14.756$ \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) $+$ $+$ $-$ $-$ \(q-q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
1848.2.a.b $1$ $14.756$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $-$ $+$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
1848.2.a.c $1$ $14.756$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $+$ \(q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots\)
1848.2.a.d $1$ $14.756$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $+$ $+$ $-$ $-$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
1848.2.a.e $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(-4\) \(-1\) $+$ $-$ $+$ $+$ \(q+q^{3}-4q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.f $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $-$ \(q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
1848.2.a.g $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $+$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.h $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $-$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1848.2.a.i $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $-$ $-$ $+$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.j $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $+$ $+$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.k $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $+$ $+$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
1848.2.a.l $1$ $14.756$ \(\Q\) None \(0\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
1848.2.a.m $2$ $14.756$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(-2\) $+$ $+$ $+$ $-$ \(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.n $2$ $14.756$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(-2\) $-$ $+$ $+$ $-$ \(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.o $2$ $14.756$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-3\) \(2\) $-$ $+$ $-$ $+$ \(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.p $2$ $14.756$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(1\) \(-2\) $+$ $+$ $+$ $+$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
1848.2.a.q $2$ $14.756$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(-2\) $-$ $+$ $+$ $+$ \(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.r $2$ $14.756$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(2\) $-$ $+$ $-$ $-$ \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.s $2$ $14.756$ \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(1\) \(-2\) $-$ $-$ $+$ $-$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
1848.2.a.t $3$ $14.756$ 3.3.961.1 None \(0\) \(3\) \(1\) \(3\) $-$ $-$ $-$ $+$ \(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1848.2.a.u $3$ $14.756$ 3.3.568.1 None \(0\) \(3\) \(1\) \(3\) $+$ $-$ $-$ $-$ \(q+q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+q^{11}+\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1848))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1848)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 2}\)