Properties

Label 1344.4.a
Level $1344$
Weight $4$
Character orbit 1344.a
Rep. character $\chi_{1344}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $48$
Sturm bound $1024$
Trace bound $11$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(1024\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1344))\).

Total New Old
Modular forms 792 72 720
Cusp forms 744 72 672
Eisenstein series 48 0 48

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(40\)
Minus space\(-\)\(32\)

Trace form

\( 72q + 648q^{9} + O(q^{10}) \) \( 72q + 648q^{9} - 208q^{17} + 1976q^{25} - 400q^{29} - 16q^{37} + 944q^{41} + 3528q^{49} + 752q^{53} - 1824q^{61} + 3072q^{65} - 1056q^{69} + 592q^{73} + 1904q^{77} + 5832q^{81} + 480q^{85} - 176q^{89} + 3632q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1344))\) 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
1344.4.a.a \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-18\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}-18q^{5}-7q^{7}+9q^{9}-72q^{11}+\cdots\)
1344.4.a.b \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-14\) \(-7\) \(+\) \(+\) \(+\) \(q-3q^{3}-14q^{5}-7q^{7}+9q^{9}-4q^{11}+\cdots\)
1344.4.a.c \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-6\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}-6q^{5}-7q^{7}+9q^{9}-4q^{11}+\cdots\)
1344.4.a.d \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-6\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}-6q^{5}-7q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
1344.4.a.e \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-4\) \(7\) \(-\) \(+\) \(-\) \(q-3q^{3}-4q^{5}+7q^{7}+9q^{9}-26q^{11}+\cdots\)
1344.4.a.f \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(-2\) \(-7\) \(+\) \(+\) \(+\) \(q-3q^{3}-2q^{5}-7q^{7}+9q^{9}+8q^{11}+\cdots\)
1344.4.a.g \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(2\) \(-7\) \(+\) \(+\) \(+\) \(q-3q^{3}+2q^{5}-7q^{7}+9q^{9}-52q^{11}+\cdots\)
1344.4.a.h \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(2\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}+2q^{5}-7q^{7}+9q^{9}+12q^{11}+\cdots\)
1344.4.a.i \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(4\) \(7\) \(-\) \(+\) \(-\) \(q-3q^{3}+4q^{5}+7q^{7}+9q^{9}+62q^{11}+\cdots\)
1344.4.a.j \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(10\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}+10q^{5}-7q^{7}+9q^{9}-12q^{11}+\cdots\)
1344.4.a.k \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(10\) \(-7\) \(+\) \(+\) \(+\) \(q-3q^{3}+10q^{5}-7q^{7}+9q^{9}+52q^{11}+\cdots\)
1344.4.a.l \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(16\) \(7\) \(+\) \(+\) \(-\) \(q-3q^{3}+2^{4}q^{5}+7q^{7}+9q^{9}+18q^{11}+\cdots\)
1344.4.a.m \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(18\) \(-7\) \(+\) \(+\) \(+\) \(q-3q^{3}+18q^{5}-7q^{7}+9q^{9}-44q^{11}+\cdots\)
1344.4.a.n \(1\) \(79.299\) \(\Q\) None \(0\) \(-3\) \(18\) \(-7\) \(-\) \(+\) \(+\) \(q-3q^{3}+18q^{5}-7q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
1344.4.a.o \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-18\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}-18q^{5}+7q^{7}+9q^{9}+72q^{11}+\cdots\)
1344.4.a.p \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-14\) \(7\) \(-\) \(-\) \(-\) \(q+3q^{3}-14q^{5}+7q^{7}+9q^{9}+4q^{11}+\cdots\)
1344.4.a.q \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-6\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}-6q^{5}+7q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
1344.4.a.r \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-6\) \(7\) \(-\) \(-\) \(-\) \(q+3q^{3}-6q^{5}+7q^{7}+9q^{9}+4q^{11}+\cdots\)
1344.4.a.s \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-4\) \(-7\) \(+\) \(-\) \(+\) \(q+3q^{3}-4q^{5}-7q^{7}+9q^{9}+26q^{11}+\cdots\)
1344.4.a.t \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(-2\) \(7\) \(-\) \(-\) \(-\) \(q+3q^{3}-2q^{5}+7q^{7}+9q^{9}-8q^{11}+\cdots\)
1344.4.a.u \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(2\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}+2q^{5}+7q^{7}+9q^{9}-12q^{11}+\cdots\)
1344.4.a.v \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(2\) \(7\) \(-\) \(-\) \(-\) \(q+3q^{3}+2q^{5}+7q^{7}+9q^{9}+52q^{11}+\cdots\)
1344.4.a.w \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(4\) \(-7\) \(+\) \(-\) \(+\) \(q+3q^{3}+4q^{5}-7q^{7}+9q^{9}-62q^{11}+\cdots\)
1344.4.a.x \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(10\) \(7\) \(-\) \(-\) \(-\) \(q+3q^{3}+10q^{5}+7q^{7}+9q^{9}-52q^{11}+\cdots\)
1344.4.a.y \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(10\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}+10q^{5}+7q^{7}+9q^{9}+12q^{11}+\cdots\)
1344.4.a.z \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(16\) \(-7\) \(-\) \(-\) \(+\) \(q+3q^{3}+2^{4}q^{5}-7q^{7}+9q^{9}-18q^{11}+\cdots\)
1344.4.a.ba \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(18\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}+18q^{5}+7q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
1344.4.a.bb \(1\) \(79.299\) \(\Q\) None \(0\) \(3\) \(18\) \(7\) \(+\) \(-\) \(-\) \(q+3q^{3}+18q^{5}+7q^{7}+9q^{9}+44q^{11}+\cdots\)
1344.4.a.bc \(2\) \(79.299\) \(\Q(\sqrt{43}) \) None \(0\) \(-6\) \(-16\) \(-14\) \(-\) \(+\) \(+\) \(q-3q^{3}+(-8+\beta )q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bd \(2\) \(79.299\) \(\Q(\sqrt{177}) \) None \(0\) \(-6\) \(-14\) \(14\) \(+\) \(+\) \(-\) \(q-3q^{3}+(-7-\beta )q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.be \(2\) \(79.299\) \(\Q(\sqrt{137}) \) None \(0\) \(-6\) \(-10\) \(14\) \(+\) \(+\) \(-\) \(q-3q^{3}+(-5-\beta )q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.bf \(2\) \(79.299\) \(\Q(\sqrt{11}) \) None \(0\) \(-6\) \(-8\) \(-14\) \(+\) \(+\) \(+\) \(q-3q^{3}+(-4+\beta )q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bg \(2\) \(79.299\) \(\Q(\sqrt{57}) \) None \(0\) \(-6\) \(-6\) \(14\) \(+\) \(+\) \(-\) \(q-3q^{3}+(-3-\beta )q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.bh \(2\) \(79.299\) \(\Q(\sqrt{37}) \) None \(0\) \(-6\) \(4\) \(14\) \(-\) \(+\) \(-\) \(q-3q^{3}+(2+\beta )q^{5}+7q^{7}+9q^{9}+(24+\cdots)q^{11}+\cdots\)
1344.4.a.bi \(2\) \(79.299\) \(\Q(\sqrt{337}) \) None \(0\) \(-6\) \(6\) \(14\) \(-\) \(+\) \(-\) \(q-3q^{3}+(3+\beta )q^{5}+7q^{7}+9q^{9}+(13+\cdots)q^{11}+\cdots\)
1344.4.a.bj \(2\) \(79.299\) \(\Q(\sqrt{17}) \) None \(0\) \(-6\) \(10\) \(14\) \(+\) \(+\) \(-\) \(q-3q^{3}+(5-\beta )q^{5}+7q^{7}+9q^{9}+(11+\cdots)q^{11}+\cdots\)
1344.4.a.bk \(2\) \(79.299\) \(\Q(\sqrt{43}) \) None \(0\) \(6\) \(-16\) \(14\) \(-\) \(-\) \(-\) \(q+3q^{3}+(-8+\beta )q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.bl \(2\) \(79.299\) \(\Q(\sqrt{177}) \) None \(0\) \(6\) \(-14\) \(-14\) \(-\) \(-\) \(+\) \(q+3q^{3}+(-7-\beta )q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bm \(2\) \(79.299\) \(\Q(\sqrt{137}) \) None \(0\) \(6\) \(-10\) \(-14\) \(+\) \(-\) \(+\) \(q+3q^{3}+(-5-\beta )q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bn \(2\) \(79.299\) \(\Q(\sqrt{11}) \) None \(0\) \(6\) \(-8\) \(14\) \(+\) \(-\) \(-\) \(q+3q^{3}+(-4+\beta )q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.bo \(2\) \(79.299\) \(\Q(\sqrt{57}) \) None \(0\) \(6\) \(-6\) \(-14\) \(-\) \(-\) \(+\) \(q+3q^{3}+(-3-\beta )q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bp \(2\) \(79.299\) \(\Q(\sqrt{37}) \) None \(0\) \(6\) \(4\) \(-14\) \(-\) \(-\) \(+\) \(q+3q^{3}+(2+\beta )q^{5}-7q^{7}+9q^{9}+(-24+\cdots)q^{11}+\cdots\)
1344.4.a.bq \(2\) \(79.299\) \(\Q(\sqrt{337}) \) None \(0\) \(6\) \(6\) \(-14\) \(+\) \(-\) \(+\) \(q+3q^{3}+(3+\beta )q^{5}-7q^{7}+9q^{9}+(-13+\cdots)q^{11}+\cdots\)
1344.4.a.br \(2\) \(79.299\) \(\Q(\sqrt{17}) \) None \(0\) \(6\) \(10\) \(-14\) \(+\) \(-\) \(+\) \(q+3q^{3}+(5-\beta )q^{5}-7q^{7}+9q^{9}+(-11+\cdots)q^{11}+\cdots\)
1344.4.a.bs \(3\) \(79.299\) 3.3.37341.1 None \(0\) \(-9\) \(-6\) \(21\) \(-\) \(+\) \(-\) \(q-3q^{3}+(-2+\beta _{1})q^{5}+7q^{7}+9q^{9}+\cdots\)
1344.4.a.bt \(3\) \(79.299\) 3.3.22700.1 None \(0\) \(-9\) \(10\) \(-21\) \(+\) \(+\) \(+\) \(q-3q^{3}+(3+\beta _{2})q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bu \(3\) \(79.299\) 3.3.37341.1 None \(0\) \(9\) \(-6\) \(-21\) \(-\) \(-\) \(+\) \(q+3q^{3}+(-2+\beta _{1})q^{5}-7q^{7}+9q^{9}+\cdots\)
1344.4.a.bv \(3\) \(79.299\) 3.3.22700.1 None \(0\) \(9\) \(10\) \(21\) \(+\) \(-\) \(-\) \(q+3q^{3}+(3+\beta _{2})q^{5}+7q^{7}+9q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1344))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1344)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 2}\)