Properties

Label 2672.2.a
Level $2672$
Weight $2$
Character orbit 2672.a
Rep. character $\chi_{2672}(1,\cdot)$
Character field $\Q$
Dimension $83$
Newform subspaces $16$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2672 = 2^{4} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2672.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2672))\).

Total New Old
Modular forms 342 83 259
Cusp forms 331 83 248
Eisenstein series 11 0 11

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

\(2\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(21\)
\(+\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(26\)
\(-\)\(-\)\(+\)\(15\)
Plus space\(+\)\(36\)
Minus space\(-\)\(47\)

Trace form

\( 83q + 2q^{3} - 2q^{5} + 2q^{7} + 79q^{9} + O(q^{10}) \) \( 83q + 2q^{3} - 2q^{5} + 2q^{7} + 79q^{9} + 2q^{11} - 2q^{13} + 12q^{15} - 2q^{17} + 10q^{19} + 8q^{23} + 77q^{25} + 20q^{27} + 6q^{29} + 10q^{31} - 8q^{33} - 2q^{37} + 4q^{39} + 6q^{41} + 12q^{43} - 10q^{45} - 10q^{47} + 83q^{49} - 20q^{51} + 6q^{53} + 12q^{55} - 8q^{57} - 10q^{61} - 14q^{63} - 4q^{65} - 28q^{67} - 4q^{71} - 2q^{73} + 26q^{75} + 8q^{77} + 8q^{79} + 59q^{81} - 8q^{83} - 28q^{85} - 12q^{87} - 2q^{89} + 20q^{91} - 16q^{93} - 12q^{95} - 2q^{97} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2672))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 167
2672.2.a.a \(1\) \(21.336\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(q+3q^{5}-q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots\)
2672.2.a.b \(2\) \(21.336\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(7\) \(+\) \(-\) \(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+(4-\beta )q^{7}+\cdots\)
2672.2.a.c \(2\) \(21.336\) \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-6\) \(-3\) \(-\) \(-\) \(q-\beta q^{3}-3q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
2672.2.a.d \(2\) \(21.336\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(6\) \(-\) \(+\) \(q+2\beta q^{3}+(1+\beta )q^{5}+3q^{7}+5q^{9}+\cdots\)
2672.2.a.e \(2\) \(21.336\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(q+\beta q^{3}-q^{5}+(1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.f \(2\) \(21.336\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(5\) \(-\) \(-\) \(q+\beta q^{3}-q^{5}+(3-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.g \(2\) \(21.336\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-4\) \(6\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-3+2\beta )q^{5}+3q^{7}+\cdots\)
2672.2.a.h \(3\) \(21.336\) 3.3.733.1 None \(0\) \(-1\) \(-3\) \(-3\) \(-\) \(-\) \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(2+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots\)
2672.2.a.i \(3\) \(21.336\) 3.3.469.1 None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
2672.2.a.j \(5\) \(21.336\) 5.5.826865.1 None \(0\) \(-3\) \(10\) \(-9\) \(-\) \(-\) \(q+(-1+\beta _{2})q^{3}+2q^{5}+(-2+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.k \(7\) \(21.336\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(4\) \(-2\) \(12\) \(-\) \(+\) \(q+(1+\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
2672.2.a.l \(7\) \(21.336\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(6\) \(0\) \(1\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.m \(9\) \(21.336\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(-8\) \(-2\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2672.2.a.n \(12\) \(21.336\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-5\) \(-2\) \(-10\) \(+\) \(+\) \(q-\beta _{1}q^{3}+\beta _{9}q^{5}+(-1-\beta _{11})q^{7}+\cdots\)
2672.2.a.o \(12\) \(21.336\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(4\) \(-11\) \(-\) \(+\) \(q-\beta _{5}q^{3}-\beta _{8}q^{5}+(-1+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
2672.2.a.p \(12\) \(21.336\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(1\) \(8\) \(4\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\)\(^{\oplus 2}\)