Properties

Label 3344.2.a
Level $3344$
Weight $2$
Character orbit 3344.a
Rep. character $\chi_{3344}(1,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $28$
Sturm bound $960$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(960\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3344))\).

Total New Old
Modular forms 492 90 402
Cusp forms 469 90 379
Eisenstein series 23 0 23

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

\(2\)\(11\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(14\)
Plus space\(+\)\(35\)
Minus space\(-\)\(55\)

Trace form

\( 90 q + 4 q^{5} + 90 q^{9} + O(q^{10}) \) \( 90 q + 4 q^{5} + 90 q^{9} - 6 q^{11} + 4 q^{13} - 12 q^{15} - 4 q^{17} + 16 q^{21} + 12 q^{23} + 86 q^{25} + 12 q^{27} + 20 q^{29} + 20 q^{37} + 24 q^{39} - 4 q^{41} + 36 q^{45} + 8 q^{47} + 90 q^{49} + 40 q^{51} + 4 q^{53} + 8 q^{55} + 40 q^{59} + 20 q^{61} + 40 q^{63} - 24 q^{65} + 16 q^{69} + 16 q^{71} - 20 q^{73} - 12 q^{75} + 74 q^{81} + 40 q^{83} + 24 q^{85} + 24 q^{87} - 36 q^{89} + 16 q^{91} - 48 q^{93} - 4 q^{97} - 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3344))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 19
3344.2.a.a 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(-3\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
3344.2.a.b 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
3344.2.a.c 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.d 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(-1\) \(-3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots\)
3344.2.a.e 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(-1\) \(2\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.f 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
3344.2.a.g 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
3344.2.a.h 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(1\) \(-2\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots\)
3344.2.a.i 3344.a 1.a $1$ $26.702$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+q^{11}-2q^{13}+\cdots\)
3344.2.a.j 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{5}+(-1+\beta )q^{7}+\beta q^{9}+\cdots\)
3344.2.a.k 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(4\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3344.2.a.l 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(3\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
3344.2.a.m 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-\beta q^{7}+2\beta q^{9}-q^{11}+\cdots\)
3344.2.a.n 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(2+\beta )q^{7}+2\beta q^{9}+\cdots\)
3344.2.a.o 3344.a 1.a $2$ $26.702$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(1+\cdots)q^{9}+\cdots\)
3344.2.a.p 3344.a 1.a $3$ $26.702$ 3.3.469.1 None \(0\) \(-1\) \(5\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3344.2.a.q 3344.a 1.a $3$ $26.702$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
3344.2.a.r 3344.a 1.a $3$ $26.702$ 3.3.229.1 None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots\)
3344.2.a.s 3344.a 1.a $4$ $26.702$ 4.4.13676.1 None \(0\) \(1\) \(-3\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
3344.2.a.t 3344.a 1.a $5$ $26.702$ 5.5.246832.1 None \(0\) \(-1\) \(-5\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3344.2.a.u 3344.a 1.a $5$ $26.702$ 5.5.3979184.1 None \(0\) \(-1\) \(7\) \(-8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(-2+\beta _{1})q^{7}+\cdots\)
3344.2.a.v 3344.a 1.a $6$ $26.702$ 6.6.576096652.1 None \(0\) \(-4\) \(1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
3344.2.a.w 3344.a 1.a $6$ $26.702$ 6.6.744786576.1 None \(0\) \(-1\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3344.2.a.x 3344.a 1.a $6$ $26.702$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3344.2.a.y 3344.a 1.a $6$ $26.702$ 6.6.57500224.1 None \(0\) \(4\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
3344.2.a.z 3344.a 1.a $6$ $26.702$ 6.6.106392688.1 None \(0\) \(4\) \(-3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots\)
3344.2.a.ba 3344.a 1.a $7$ $26.702$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-2\) \(2\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-2-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
3344.2.a.bb 3344.a 1.a $9$ $26.702$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-1\) \(6\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{7})q^{5}-\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3344))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3344)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(836))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1672))\)\(^{\oplus 2}\)