Properties

Label 4275.2.a
Level $4275$
Weight $2$
Character orbit 4275.a
Rep. character $\chi_{4275}(1,\cdot)$
Character field $\Q$
Dimension $142$
Newform subspaces $50$
Sturm bound $1200$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4275.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 50 \)
Sturm bound: \(1200\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4275))\).

Total New Old
Modular forms 624 142 482
Cusp forms 577 142 435
Eisenstein series 47 0 47

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

\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(-\)\(-\)\(16\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(25\)
Plus space\(+\)\(62\)
Minus space\(-\)\(80\)

Trace form

\( 142q + q^{2} + 143q^{4} + 5q^{7} - 3q^{8} + O(q^{10}) \) \( 142q + q^{2} + 143q^{4} + 5q^{7} - 3q^{8} + 13q^{11} - 2q^{13} - 12q^{14} + 145q^{16} - 11q^{17} - 2q^{19} + 4q^{22} - 8q^{23} + 6q^{26} + 18q^{28} + 32q^{29} + 5q^{32} + 18q^{34} - 12q^{37} - 3q^{38} + 13q^{43} + 66q^{44} + 36q^{46} - q^{47} + 145q^{49} + 14q^{52} + 26q^{53} + 8q^{56} + 10q^{58} - 18q^{59} - 9q^{61} + 8q^{62} + 185q^{64} + 12q^{67} - 52q^{68} - 42q^{71} + q^{73} + 62q^{74} - 5q^{76} - 41q^{77} + 8q^{79} + 38q^{82} + 16q^{83} + 4q^{86} - 32q^{88} - 2q^{89} - 16q^{91} + 40q^{92} - 32q^{94} - 6q^{97} + 5q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 19
4275.2.a.a \(1\) \(34.136\) \(\Q\) None \(-2\) \(0\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-3q^{7}+3q^{11}+6q^{13}+\cdots\)
4275.2.a.b \(1\) \(34.136\) \(\Q\) None \(-2\) \(0\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q-2q^{2}+2q^{4}+5q^{7}-q^{11}-2q^{13}+\cdots\)
4275.2.a.c \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}-4q^{7}+3q^{8}-3q^{11}+\cdots\)
4275.2.a.d \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}-2q^{7}+3q^{8}-2q^{11}+\cdots\)
4275.2.a.e \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots\)
4275.2.a.f \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-5q^{11}-4q^{13}+\cdots\)
4275.2.a.g \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}+2q^{7}+3q^{8}+2q^{11}+\cdots\)
4275.2.a.h \(1\) \(34.136\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}+2q^{7}+3q^{8}+6q^{11}+\cdots\)
4275.2.a.i \(1\) \(34.136\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q-2q^{4}+q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
4275.2.a.j \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots\)
4275.2.a.k \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}-2q^{7}-3q^{8}+2q^{11}+\cdots\)
4275.2.a.l \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-5q^{11}+4q^{13}+\cdots\)
4275.2.a.m \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-6q^{13}-q^{16}+\cdots\)
4275.2.a.n \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-2q^{11}+\cdots\)
4275.2.a.o \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}+2q^{7}-3q^{8}+2q^{11}+\cdots\)
4275.2.a.p \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+2q^{7}-3q^{8}+4q^{11}+\cdots\)
4275.2.a.q \(1\) \(34.136\) \(\Q\) None \(1\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{11}+\cdots\)
4275.2.a.r \(2\) \(34.136\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-2\beta )q^{7}+\cdots\)
4275.2.a.s \(2\) \(34.136\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
4275.2.a.t \(2\) \(34.136\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}+(1-\beta )q^{7}-\beta q^{8}+(-3+\cdots)q^{11}+\cdots\)
4275.2.a.u \(2\) \(34.136\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+5q^{4}+(1+\beta )q^{7}+3\beta q^{8}+\cdots\)
4275.2.a.v \(2\) \(34.136\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
4275.2.a.w \(2\) \(34.136\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots\)
4275.2.a.x \(2\) \(34.136\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2-\beta )q^{7}+\cdots\)
4275.2.a.y \(2\) \(34.136\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+\beta q^{7}+(3+\cdots)q^{8}+\cdots\)
4275.2.a.z \(3\) \(34.136\) \(\Q(\zeta_{14})^+\) None \(-4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
4275.2.a.ba \(3\) \(34.136\) 3.3.169.1 None \(-2\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4275.2.a.bb \(3\) \(34.136\) 3.3.148.1 None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(-1+\cdots)q^{8}+\cdots\)
4275.2.a.bc \(3\) \(34.136\) 3.3.148.1 None \(-1\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bd \(3\) \(34.136\) 3.3.148.1 None \(-1\) \(0\) \(0\) \(8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(3-\beta _{1})q^{7}+\cdots\)
4275.2.a.be \(3\) \(34.136\) 3.3.621.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{7}+\cdots\)
4275.2.a.bf \(3\) \(34.136\) 3.3.837.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4275.2.a.bg \(3\) \(34.136\) 3.3.837.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bh \(3\) \(34.136\) 3.3.621.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+\cdots\)
4275.2.a.bi \(3\) \(34.136\) 3.3.148.1 None \(1\) \(0\) \(0\) \(-8\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bj \(3\) \(34.136\) 3.3.148.1 None \(1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots\)
4275.2.a.bk \(3\) \(34.136\) 3.3.148.1 None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-2\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots\)
4275.2.a.bl \(3\) \(34.136\) 3.3.148.1 None \(1\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4275.2.a.bm \(3\) \(34.136\) 3.3.169.1 None \(2\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
4275.2.a.bn \(3\) \(34.136\) \(\Q(\zeta_{14})^+\) None \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bo \(4\) \(34.136\) 4.4.11344.1 None \(-2\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
4275.2.a.bp \(4\) \(34.136\) 4.4.13068.1 None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-1+\beta _{3})q^{7}+\cdots\)
4275.2.a.bq \(6\) \(34.136\) 6.6.15044092.1 None \(0\) \(0\) \(0\) \(-8\) \(+\) \(-\) \(-\) \(q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(-1+\beta _{1}-\beta _{5})q^{7}+\cdots\)
4275.2.a.br \(6\) \(34.136\) 6.6.66064384.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
4275.2.a.bs \(6\) \(34.136\) 6.6.16717036.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
4275.2.a.bt \(6\) \(34.136\) 6.6.16717036.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{2}-\beta _{4})q^{7}+\cdots\)
4275.2.a.bu \(6\) \(34.136\) 6.6.15044092.1 None \(0\) \(0\) \(0\) \(8\) \(+\) \(+\) \(-\) \(q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(1-\beta _{1}+\beta _{5})q^{7}+\cdots\)
4275.2.a.bv \(7\) \(34.136\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(0\) \(0\) \(8\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{7}+\cdots\)
4275.2.a.bw \(7\) \(34.136\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(0\) \(0\) \(-8\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
4275.2.a.bx \(12\) \(34.136\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{5}q^{2}+(1+\beta _{6})q^{4}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\)\(^{\oplus 2}\)