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Properties

Label 2673.2.a
Level $2673$
Weight $2$
Character orbit 2673.a
Rep. character $\chi_{2673}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $18$
Sturm bound $648$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 2673 = 3^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2673.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(648\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2673))\).

Total New Old
Modular forms 342 120 222
Cusp forms 307 120 187
Eisenstein series 35 0 35

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

\(3\)\(11\)FrickeDim
\(+\)\(+\)$+$\(29\)
\(+\)\(-\)$-$\(35\)
\(-\)\(+\)$-$\(31\)
\(-\)\(-\)$+$\(25\)
Plus space\(+\)\(54\)
Minus space\(-\)\(66\)

Trace form

\( 120 q + 120 q^{4} + 6 q^{7} + O(q^{10}) \) \( 120 q + 120 q^{4} + 6 q^{7} + 6 q^{13} + 120 q^{16} + 6 q^{19} + 120 q^{25} + 24 q^{28} + 24 q^{31} + 36 q^{34} + 6 q^{37} + 36 q^{40} + 24 q^{43} + 36 q^{46} + 126 q^{49} + 24 q^{52} - 48 q^{61} + 156 q^{64} - 48 q^{67} - 48 q^{73} + 60 q^{76} + 6 q^{79} - 144 q^{82} - 144 q^{85} - 24 q^{91} - 138 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2673))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
2673.2.a.a 2673.a 1.a $4$ $21.344$ 4.4.4752.1 None \(-2\) \(0\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
2673.2.a.b 2673.a 1.a $4$ $21.344$ 4.4.4752.1 None \(-2\) \(0\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
2673.2.a.c 2673.a 1.a $4$ $21.344$ 4.4.4752.1 None \(2\) \(0\) \(2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
2673.2.a.d 2673.a 1.a $4$ $21.344$ 4.4.4752.1 None \(2\) \(0\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2673.2.a.e 2673.a 1.a $5$ $21.344$ 5.5.760752.1 None \(-2\) \(0\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\beta _{4}q^{7}+\cdots\)
2673.2.a.f 2673.a 1.a $5$ $21.344$ 5.5.3037392.1 None \(-2\) \(0\) \(-2\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2673.2.a.g 2673.a 1.a $5$ $21.344$ 5.5.760752.1 None \(2\) \(0\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+\beta _{4}q^{7}+\cdots\)
2673.2.a.h 2673.a 1.a $5$ $21.344$ 5.5.3037392.1 None \(2\) \(0\) \(2\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2673.2.a.i 2673.a 1.a $6$ $21.344$ 6.6.110071872.1 None \(-2\) \(0\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
2673.2.a.j 2673.a 1.a $6$ $21.344$ 6.6.864654912.1 None \(-2\) \(0\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{4}q^{7}+\cdots\)
2673.2.a.k 2673.a 1.a $6$ $21.344$ 6.6.3916917.1 None \(0\) \(0\) \(-6\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
2673.2.a.l 2673.a 1.a $6$ $21.344$ 6.6.3916917.1 None \(0\) \(0\) \(6\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{4})q^{2}-\beta _{2}q^{4}+(1+\beta _{3})q^{5}+\cdots\)
2673.2.a.m 2673.a 1.a $6$ $21.344$ 6.6.1397493.1 None \(0\) \(0\) \(0\) \(-9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
2673.2.a.n 2673.a 1.a $6$ $21.344$ 6.6.1397493.1 None \(0\) \(0\) \(0\) \(-9\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2673.2.a.o 2673.a 1.a $6$ $21.344$ 6.6.110071872.1 None \(2\) \(0\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
2673.2.a.p 2673.a 1.a $6$ $21.344$ 6.6.864654912.1 None \(2\) \(0\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}-\beta _{4}q^{7}+\cdots\)
2673.2.a.q 2673.a 1.a $18$ $21.344$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(-6\) \(21\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots\)
2673.2.a.r 2673.a 1.a $18$ $21.344$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(6\) \(21\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2673))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2673)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 2}\)