Properties

Label 2300.2.a
Level $2300$
Weight $2$
Character orbit 2300.a
Rep. character $\chi_{2300}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $15$
Sturm bound $720$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(720\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2300))\).

Total New Old
Modular forms 378 36 342
Cusp forms 343 36 307
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.

\(2\)\(5\)\(23\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(18\)
Minus space\(-\)\(18\)

Trace form

\( 36 q - 2 q^{3} + 6 q^{7} + 34 q^{9} + O(q^{10}) \) \( 36 q - 2 q^{3} + 6 q^{7} + 34 q^{9} - 6 q^{11} + 6 q^{13} - 10 q^{17} + 4 q^{19} - 2 q^{21} - 2 q^{27} - 18 q^{29} + 10 q^{31} + 6 q^{33} + 10 q^{37} + 6 q^{39} - 14 q^{41} - 6 q^{47} + 56 q^{49} - 18 q^{51} - 4 q^{53} - 8 q^{57} - 28 q^{59} + 8 q^{63} - 10 q^{67} + 4 q^{69} - 10 q^{71} + 14 q^{73} - 20 q^{77} + 12 q^{81} - 10 q^{83} - 22 q^{87} - 12 q^{89} - 22 q^{91} + 6 q^{93} + 18 q^{97} - 80 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
2300.2.a.a 2300.a 1.a $1$ $18.366$ \(\Q\) None 460.2.a.d \(0\) \(-3\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
2300.2.a.b 2300.a 1.a $1$ $18.366$ \(\Q\) None 2300.2.a.b \(0\) \(-2\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
2300.2.a.c 2300.a 1.a $1$ $18.366$ \(\Q\) None 92.2.a.b \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
2300.2.a.d 2300.a 1.a $1$ $18.366$ \(\Q\) None 460.2.a.c \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}-2q^{9}-6q^{11}+q^{13}+\cdots\)
2300.2.a.e 2300.a 1.a $1$ $18.366$ \(\Q\) None 460.2.a.b \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+6q^{11}-6q^{13}-7q^{17}+\cdots\)
2300.2.a.f 2300.a 1.a $1$ $18.366$ \(\Q\) None 460.2.a.a \(0\) \(1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}-4q^{11}-q^{13}+\cdots\)
2300.2.a.g 2300.a 1.a $1$ $18.366$ \(\Q\) None 2300.2.a.b \(0\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
2300.2.a.h 2300.a 1.a $1$ $18.366$ \(\Q\) None 92.2.a.a \(0\) \(3\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{7}+6q^{9}+2q^{11}+5q^{13}+\cdots\)
2300.2.a.i 2300.a 1.a $2$ $18.366$ \(\Q(\sqrt{17}) \) None 460.2.a.e \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
2300.2.a.j 2300.a 1.a $3$ $18.366$ 3.3.321.1 None 2300.2.a.j \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2300.2.a.k 2300.a 1.a $3$ $18.366$ 3.3.321.1 None 2300.2.a.j \(0\) \(2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
2300.2.a.l 2300.a 1.a $4$ $18.366$ 4.4.53121.1 None 2300.2.a.l \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.a.m 2300.a 1.a $4$ $18.366$ 4.4.53121.1 None 2300.2.a.l \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2300.2.a.n 2300.a 1.a $6$ $18.366$ 6.6.143376304.1 None 460.2.c.a \(0\) \(-4\) \(0\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
2300.2.a.o 2300.a 1.a $6$ $18.366$ 6.6.143376304.1 None 460.2.c.a \(0\) \(4\) \(0\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2300)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 2}\)