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Properties

Label 2275.2.a
Level $2275$
Weight $2$
Character orbit 2275.a
Rep. character $\chi_{2275}(1,\cdot)$
Character field $\Q$
Dimension $114$
Newform subspaces $28$
Sturm bound $560$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2275 = 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2275.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(560\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2275))\).

Total New Old
Modular forms 292 114 178
Cusp forms 269 114 155
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.

\(5\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(14\)
\(+\)\(+\)\(-\)$-$\(16\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(11\)
\(-\)\(+\)\(+\)$-$\(16\)
\(-\)\(+\)\(-\)$+$\(12\)
\(-\)\(-\)\(+\)$+$\(14\)
\(-\)\(-\)\(-\)$-$\(18\)
Plus space\(+\)\(51\)
Minus space\(-\)\(63\)

Trace form

\( 114 q - 4 q^{2} + 120 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{8} + 106 q^{9} + O(q^{10}) \) \( 114 q - 4 q^{2} + 120 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{8} + 106 q^{9} + 12 q^{12} - 2 q^{14} + 132 q^{16} - 16 q^{17} + 8 q^{18} + 4 q^{21} - 8 q^{22} - 2 q^{23} + 40 q^{24} + 12 q^{27} - 14 q^{28} - 10 q^{29} + 20 q^{31} - 8 q^{32} - 44 q^{33} + 28 q^{34} + 144 q^{36} - 4 q^{37} + 44 q^{38} + 8 q^{39} - 40 q^{41} + 20 q^{42} - 10 q^{43} + 12 q^{46} + 24 q^{47} + 56 q^{48} + 114 q^{49} - 56 q^{51} + 8 q^{52} + 14 q^{53} - 32 q^{54} - 30 q^{56} - 32 q^{57} - 4 q^{58} - 60 q^{59} + 20 q^{61} + 48 q^{62} - 18 q^{63} + 144 q^{64} + 12 q^{66} - 28 q^{67} - 28 q^{68} + 20 q^{69} - 40 q^{71} + 76 q^{72} - 64 q^{73} + 4 q^{74} + 20 q^{76} - 8 q^{77} - 4 q^{78} + 6 q^{79} - 6 q^{81} + 16 q^{82} - 36 q^{83} + 12 q^{84} + 16 q^{86} + 56 q^{87} - 48 q^{89} + 4 q^{91} + 100 q^{92} + 52 q^{93} - 60 q^{94} + 40 q^{96} - 24 q^{97} - 4 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2275))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 13
2275.2.a.a 2275.a 1.a $1$ $18.166$ \(\Q\) None \(-2\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}-2q^{9}+\cdots\)
2275.2.a.b 2275.a 1.a $1$ $18.166$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-q^{7}+3q^{8}+\cdots\)
2275.2.a.c 2275.a 1.a $1$ $18.166$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{9}+q^{13}+\cdots\)
2275.2.a.d 2275.a 1.a $1$ $18.166$ \(\Q\) None \(0\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-q^{7}+q^{9}-4q^{12}+\cdots\)
2275.2.a.e 2275.a 1.a $1$ $18.166$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}-q^{13}+\cdots\)
2275.2.a.f 2275.a 1.a $1$ $18.166$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+q^{7}-3q^{8}+\cdots\)
2275.2.a.g 2275.a 1.a $1$ $18.166$ \(\Q\) None \(2\) \(-1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{7}-2q^{9}+\cdots\)
2275.2.a.h 2275.a 1.a $1$ $18.166$ \(\Q\) None \(2\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{7}-3q^{9}-6q^{11}+\cdots\)
2275.2.a.i 2275.a 1.a $2$ $18.166$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
2275.2.a.j 2275.a 1.a $2$ $18.166$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}-2q^{6}-q^{7}-2\beta q^{8}+\cdots\)
2275.2.a.k 2275.a 1.a $2$ $18.166$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-\beta q^{3}+(2+2\beta )q^{4}+(-3+\cdots)q^{6}+\cdots\)
2275.2.a.l 2275.a 1.a $3$ $18.166$ 3.3.169.1 None \(-2\) \(-1\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
2275.2.a.m 2275.a 1.a $3$ $18.166$ 3.3.316.1 None \(-1\) \(2\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2275.2.a.n 2275.a 1.a $3$ $18.166$ 3.3.169.1 None \(2\) \(1\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
2275.2.a.o 2275.a 1.a $4$ $18.166$ 4.4.1957.1 None \(-3\) \(-4\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
2275.2.a.p 2275.a 1.a $4$ $18.166$ 4.4.12197.1 None \(1\) \(0\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2275.2.a.q 2275.a 1.a $5$ $18.166$ 5.5.138917.1 None \(-2\) \(-3\) \(0\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2}-\beta _{4})q^{4}+\cdots\)
2275.2.a.r 2275.a 1.a $5$ $18.166$ 5.5.138917.1 None \(2\) \(3\) \(0\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2}-\beta _{4})q^{4}+\cdots\)
2275.2.a.s 2275.a 1.a $6$ $18.166$ 6.6.45853772.1 None \(-3\) \(0\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
2275.2.a.t 2275.a 1.a $6$ $18.166$ 6.6.134584629.1 None \(-1\) \(-2\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2275.2.a.u 2275.a 1.a $6$ $18.166$ 6.6.134584629.1 None \(1\) \(2\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2275.2.a.v 2275.a 1.a $7$ $18.166$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-3\) \(0\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(-\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
2275.2.a.w 2275.a 1.a $7$ $18.166$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-2\) \(0\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
2275.2.a.x 2275.a 1.a $7$ $18.166$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(0\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
2275.2.a.y 2275.a 1.a $7$ $18.166$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(2\) \(0\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
2275.2.a.z 2275.a 1.a $7$ $18.166$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(3\) \(0\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
2275.2.a.ba 2275.a 1.a $10$ $18.166$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(4\) \(0\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2275.2.a.bb 2275.a 1.a $10$ $18.166$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-4\) \(0\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 2}\)