Properties

Label 2299.2.a
Level $2299$
Weight $2$
Character orbit 2299.a
Rep. character $\chi_{2299}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $25$
Sturm bound $440$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2299 = 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2299.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(440\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2299))\).

Total New Old
Modular forms 232 164 68
Cusp forms 209 164 45
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.

\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(38\)
\(+\)\(-\)\(-\)\(46\)
\(-\)\(+\)\(-\)\(45\)
\(-\)\(-\)\(+\)\(35\)
Plus space\(+\)\(73\)
Minus space\(-\)\(91\)

Trace form

\( 164 q - q^{2} - 2 q^{3} + 163 q^{4} + 3 q^{5} + 8 q^{6} - 7 q^{7} + 3 q^{8} + 164 q^{9} - 6 q^{10} + 6 q^{13} + 4 q^{14} - 18 q^{15} + 137 q^{16} + q^{17} + 3 q^{18} - 2 q^{19} - 4 q^{20} - 2 q^{21} - 12 q^{23}+ \cdots - 25 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2299))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 19
2299.2.a.a 2299.a 1.a $1$ $18.358$ \(\Q\) None 2299.2.a.a \(-2\) \(-3\) \(-3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}-3q^{5}+6q^{6}+\cdots\)
2299.2.a.b 2299.a 1.a $1$ $18.358$ \(\Q\) None 19.2.a.a \(0\) \(-2\) \(3\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
2299.2.a.c 2299.a 1.a $1$ $18.358$ \(\Q\) None 209.2.a.a \(0\) \(1\) \(-3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}+4q^{7}-2q^{9}+\cdots\)
2299.2.a.d 2299.a 1.a $1$ $18.358$ \(\Q\) None 2299.2.a.a \(2\) \(-3\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+2q^{4}-3q^{5}-6q^{6}+\cdots\)
2299.2.a.e 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{3}) \) None 2299.2.a.e \(-2\) \(0\) \(6\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
2299.2.a.f 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{2}) \) None 209.2.a.b \(0\) \(-2\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}-q^{5}+(2-\beta )q^{6}+\cdots\)
2299.2.a.g 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{5}) \) None 209.2.f.a \(0\) \(2\) \(-1\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+2\beta q^{3}+3q^{4}-\beta q^{5}+\cdots\)
2299.2.a.h 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{5}) \) None 209.2.f.a \(0\) \(2\) \(-1\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+(2-2\beta )q^{3}+3q^{4}+(-1+\cdots)q^{5}+\cdots\)
2299.2.a.i 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{5}) \) None 2299.2.a.i \(0\) \(3\) \(-1\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+(1+\beta )q^{3}+3q^{4}+(-1+\cdots)q^{5}+\cdots\)
2299.2.a.j 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{5}) \) None 2299.2.a.i \(0\) \(3\) \(-1\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+(2-\beta )q^{3}+3q^{4}-\beta q^{5}+\cdots\)
2299.2.a.k 2299.a 1.a $2$ $18.358$ \(\Q(\sqrt{3}) \) None 2299.2.a.e \(2\) \(0\) \(6\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-\beta q^{3}+(2+2\beta )q^{4}+3q^{5}+\cdots\)
2299.2.a.l 2299.a 1.a $3$ $18.358$ 3.3.1229.1 None 2299.2.a.l \(-3\) \(-1\) \(1\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
2299.2.a.m 2299.a 1.a $3$ $18.358$ 3.3.1229.1 None 2299.2.a.l \(3\) \(-1\) \(1\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
2299.2.a.n 2299.a 1.a $5$ $18.358$ 5.5.246832.1 None 209.2.a.c \(-2\) \(1\) \(-5\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
2299.2.a.o 2299.a 1.a $7$ $18.358$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2299.2.a.o \(-4\) \(-1\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots\)
2299.2.a.p 2299.a 1.a $7$ $18.358$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2299.2.a.p \(-2\) \(-1\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
2299.2.a.q 2299.a 1.a $7$ $18.358$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 209.2.a.d \(1\) \(2\) \(2\) \(-10\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
2299.2.a.r 2299.a 1.a $7$ $18.358$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2299.2.a.p \(2\) \(-1\) \(-1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
2299.2.a.s 2299.a 1.a $7$ $18.358$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2299.2.a.o \(4\) \(-1\) \(-1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots\)
2299.2.a.t 2299.a 1.a $14$ $18.358$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 209.2.f.b \(-1\) \(-2\) \(-14\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2299.2.a.u 2299.a 1.a $14$ $18.358$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 209.2.f.b \(1\) \(-2\) \(-14\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2299.2.a.v 2299.a 1.a $16$ $18.358$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 2299.2.a.v \(-6\) \(-2\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2299.2.a.w 2299.a 1.a $16$ $18.358$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 2299.2.a.v \(6\) \(-2\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2299.2.a.x 2299.a 1.a $20$ $18.358$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 209.2.f.c \(-1\) \(4\) \(18\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
2299.2.a.y 2299.a 1.a $20$ $18.358$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 209.2.f.c \(1\) \(4\) \(18\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2299))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2299)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)