Properties

Label 7448.2.a
Level $7448$
Weight $2$
Character orbit 7448.a
Rep. character $\chi_{7448}(1,\cdot)$
Character field $\Q$
Dimension $185$
Newform subspaces $50$
Sturm bound $2240$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 50 \)
Sturm bound: \(2240\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7448))\).

Total New Old
Modular forms 1152 185 967
Cusp forms 1089 185 904
Eisenstein series 63 0 63

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

\(2\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(23\)
\(+\)\(+\)\(-\)\(-\)\(23\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(23\)
\(-\)\(+\)\(+\)\(-\)\(26\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(28\)
Plus space\(+\)\(85\)
Minus space\(-\)\(100\)

Trace form

\( 185 q - 4 q^{5} + 183 q^{9} + O(q^{10}) \) \( 185 q - 4 q^{5} + 183 q^{9} - 6 q^{11} + 2 q^{13} - 16 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{23} + 201 q^{25} - 24 q^{27} + 14 q^{29} + 4 q^{31} + 4 q^{33} - 14 q^{37} + 26 q^{39} - 2 q^{41} - 14 q^{43} - 16 q^{45} - 30 q^{47} + 4 q^{51} + 10 q^{53} - 6 q^{55} + 2 q^{57} - 8 q^{59} - 24 q^{61} + 16 q^{65} - 20 q^{67} + 20 q^{69} + 8 q^{71} + 14 q^{73} - 20 q^{75} - 20 q^{79} + 169 q^{81} + 40 q^{83} + 42 q^{85} + 10 q^{87} + 14 q^{89} + 4 q^{93} + 22 q^{97} + 62 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7448))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 19
7448.2.a.a \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{3}-q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
7448.2.a.b \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
7448.2.a.c \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q-2q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7448.2.a.d \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{5}+q^{9}-3q^{11}-6q^{13}+\cdots\)
7448.2.a.e \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{3}+q^{5}+q^{9}+3q^{11}+2q^{13}+\cdots\)
7448.2.a.f \(1\) \(59.473\) \(\Q\) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
7448.2.a.g \(1\) \(59.473\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{9}+2q^{11}-q^{13}+5q^{17}+\cdots\)
7448.2.a.h \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q-3q^{5}-3q^{9}-q^{11}+6q^{17}+q^{19}+\cdots\)
7448.2.a.i \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{5}-3q^{9}-q^{11}+2q^{13}+2q^{17}+\cdots\)
7448.2.a.j \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-3q^{5}-3q^{9}+5q^{11}+4q^{13}-2q^{17}+\cdots\)
7448.2.a.k \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{5}-3q^{9}-q^{11}-2q^{13}+3q^{17}+\cdots\)
7448.2.a.l \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{5}-3q^{9}-q^{11}+2q^{13}-3q^{17}+\cdots\)
7448.2.a.m \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{5}-3q^{9}-q^{11}-2q^{13}-2q^{17}+\cdots\)
7448.2.a.n \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q+3q^{5}-3q^{9}-q^{11}-6q^{17}-q^{19}+\cdots\)
7448.2.a.o \(1\) \(59.473\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q+3q^{5}-3q^{9}+5q^{11}-4q^{13}+2q^{17}+\cdots\)
7448.2.a.p \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
7448.2.a.q \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{5}+q^{9}-3q^{11}+6q^{13}+\cdots\)
7448.2.a.r \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}-q^{5}+q^{9}+3q^{11}-2q^{13}+\cdots\)
7448.2.a.s \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7448.2.a.t \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q+2q^{3}+q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7448.2.a.u \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
7448.2.a.v \(1\) \(59.473\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
7448.2.a.w \(2\) \(59.473\) \(\Q(\sqrt{57}) \) None \(0\) \(-4\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{3}-q^{5}+q^{9}+(-1-\beta )q^{11}+\cdots\)
7448.2.a.x \(2\) \(59.473\) \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+(-2+\beta )q^{3}+q^{5}+(3-4\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
7448.2.a.y \(2\) \(59.473\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-5\) \(0\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(-2-\beta )q^{5}+(-1+\cdots)q^{9}+\cdots\)
7448.2.a.z \(2\) \(59.473\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-\beta q^{3}+q^{5}+(-2+\beta )q^{9}+(1-3\beta )q^{11}+\cdots\)
7448.2.a.ba \(2\) \(59.473\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+(1-2\beta )q^{5}+(-2+\beta )q^{9}+\cdots\)
7448.2.a.bb \(2\) \(59.473\) \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{3}+q^{5}+\beta q^{9}+(-1+\beta )q^{11}+\cdots\)
7448.2.a.bc \(2\) \(59.473\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+(-1+3\beta )q^{9}+\cdots\)
7448.2.a.bd \(2\) \(59.473\) \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(1-3\beta )q^{11}+\cdots\)
7448.2.a.be \(2\) \(59.473\) \(\Q(\sqrt{57}) \) None \(0\) \(4\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
7448.2.a.bf \(3\) \(59.473\) 3.3.961.1 None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(5-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7448.2.a.bg \(3\) \(59.473\) 3.3.1076.1 None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bh \(3\) \(59.473\) 3.3.1076.1 None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bi \(3\) \(59.473\) 3.3.1101.1 None \(0\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
7448.2.a.bj \(4\) \(59.473\) 4.4.25857.1 None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
7448.2.a.bk \(4\) \(59.473\) 4.4.18097.1 None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bl \(5\) \(59.473\) 5.5.10463409.1 None \(0\) \(0\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7448.2.a.bm \(6\) \(59.473\) 6.6.98211824.1 None \(0\) \(-3\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7448.2.a.bn \(6\) \(59.473\) 6.6.98211824.1 None \(0\) \(3\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7448.2.a.bo \(7\) \(59.473\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{5}q^{5}+(1+\beta _{4}+\beta _{5})q^{9}+\cdots\)
7448.2.a.bp \(7\) \(59.473\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{4}+\beta _{5})q^{9}+\cdots\)
7448.2.a.bq \(8\) \(59.473\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{9}+(1+\beta _{3}+\cdots)q^{11}+\cdots\)
7448.2.a.br \(8\) \(59.473\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{2})q^{9}+(1+\beta _{3}+\cdots)q^{11}+\cdots\)
7448.2.a.bs \(11\) \(59.473\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)
7448.2.a.bt \(11\) \(59.473\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)
7448.2.a.bu \(14\) \(59.473\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-6\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7448.2.a.bv \(14\) \(59.473\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7448.2.a.bw \(14\) \(59.473\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7448.2.a.bx \(14\) \(59.473\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(6\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7448))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7448)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3724))\)\(^{\oplus 2}\)